How To Find The Length And Width Of A Rectangle When Given The Perimeter And Area
This article is all about how to find the length and width of a rectangle when given the area, how to find the perimeter of a rectangle with only the area, how to find the width of a rectangle if you know its length and area, how to find the dimensions of a rectangle given the area, How To Find The Perimeter Of A Rectangle With Only The Area and many more.
Example: The perimeter of a rectangle is 26 m while the area is 42 m². Calculate the length and width dimensions of this rectangle.
Solution: The information we were given above tells us that the area of the rectangle is 42 m² while the perimeter of the same rectangle stands at 26 meters. To find sizes of the length and width of this rectangle, we need to apply the formulas for finding the perimeter and area of a rectangle respectively as follows:
Perimeter Of Rectangle = 2 x (Length + Width)
26 = 2 x (L + W)
26 ÷ 2 = [2 x (L + W)] ÷ 2
13 = (L + W)
W = 13 – L
But Area Of Rectangle = Length (L) x Width (W)
Form the information given, we have as follows:
42 = L x W
Substituting the W = 13 – L into the formula, we have as follows:
42 = L (13 – L)
42 = 13L – L²
L² – 13L + 42 = 0
(L – 7) (L – 6) = 0
So if L – 7 = 0, then L = 7.
If (L – 6) = 0, then L = 6
Thus, the length and width dimensions of a rectangle which has an area of 42 cm² and a perimeter of 26 cm are 6 cm and 7 cm respectively.
How To Find The Length Of A Rectangle When Given The Area And Width
How To Find The Length And Width Of A Rectangle When Given The Perimeter And Area – Recall that the area of rectangle can be defines as that total region or space covered by the four sides of a rectangle. The Area Of Rectangle Formula is given as follows:
Area Of A Rectangle = Length x Width
In some questions or examinations, school students can be given the value for the area of a rectangle and also the value for either the length or width of the rectangle as the case may be. Then, the examiner will task the students to solve for the value of the remaining side of the rectangle which is not given. In such a case, the student simply needs to appropriately substitute the values given in the question into the formula for finding area of a rectangle. Therefrom, he can now compute for the values of that were not given.
Example: Compute the length of a rectangular shaped screen if the width is 20 cm and the area covered by the screen is 220 cm².
Solution: How To Find The Length And Width Of A Rectangle When Given The Perimeter And Area – From the information given above, we were simply asked to compute the length of the screen whose area is 220 cm² and width is 20 cm.
Area Of A Rectangle = Length x Width
220 = Length x 20
Length = 220 ÷ 20
Therefore, the length of the screen is = 11 cm
How To Find The Width Of A Rectangle If You Know Its Length And Area
How To Find The Length And Width Of A Rectangle When Given The Perimeter And Area
In some questions regarding the area of a rectangle, you can be given the dimension of the length of the rectangle as well its area. Then you will be required to work for the value of the width of the figure. What you will simply do is to put the values you were given into the Area Of Rectangle Calculator Formula and solve it down to arrive at the value of the width. See the instance given below.
Example: The area of a rectangular wall which is 75 cm long is given as 150 cm². Find the dimension of the other side of this rectangular wall.
Solution: How To Find The Length And Width Of A Rectangle When Given The Perimeter And Area – In the above question, we were given the value of the area of the rectangular wall as 150 cm² and also, the measurement of the length of the wall as 75 cm. Common sense tells us that what we were asked to solve for is the width or breadth of the rectangular wall. What we are going to do here is to substitute the values we have into the formula for finding the area of a rectangle. From there, we will derive the dimension of the width of the rectangular wall as follows:
Area Of A Rectangle = Length x Width
So we have 150 = 75 x Width
Width = 150 ÷ 75
Therefore, the Width of the rectangular wall is = 2 cm. This is How To Find The Length And Width Of A Rectangle When Given The Perimeter And Area.
What Is The Area Of A Rectangle With A Width of 12 Feet And A Length Of 10 Feet
How To Find The Length And Width Of A Rectangle When Given The Perimeter And Area
Area Of Rectangle Formula = Length x Width
Area Of Rectangle = 10 x 12
Area Of Rectangle = 120 ft²
What Is The Formula For Finding The Area Of A Rectangle
How To Find The Length And Width Of A Rectangle When Given The Perimeter And Area
The area of a rectangle measures the total region or space covered by the four sides of a rectangle. The formula for finding the area of a rectangle is given as:
Area Of Rectangle Formula = Length x Width
What Is The Area Of A Rectangle That Is 8 Inches Wide And 12 Inches Long?
How To Find The Length And Width Of A Rectangle When Given The Perimeter And Area
Area Of Rectangle Formula = Length x Width
Area Of Rectangle = 12 x 8
Area Of Rectangle = 96 inch²
Find The Dimensions Of A Rectangle With Area 1000 m² Whose Perimeter Is As Small As Possible
How To Find The Length And Width Of A Rectangle When Given The Perimeter And Area – To find the dimensions of a rectangle with an area 1,000m² whose perimeter is as small as possible, we solve as follows:
Let the length of the rectangle be called L and the width of the rectangle be known as W.
Area of rectangle (A) = LW m² = 1000 m² — (Equation 1)
Perimeter of rectangle (P) = 2 (L + W) m — (Equation 2)
We were given the area of the rectangle, so our primary objective is to find the minimum values that will give us the minimum perimeter of this rectangle. So from equation above, we can derive the third equation as follows:
W = 1000/L — ( Equation 3)
We will substitute equation (3) in equation (2) to have:
P = 2(L + 1000/L)
P = 2L + 2000/L
We need to go further to differentiate the equation above so as arrive at the minimum area as follows:
dP/dL = 2 – 2000/L²
Equating the above statement to zero, we have:
2 – 2000/L² = 0
2 = 2000/L²
L² = 1000
L = √1000
W = 1000/L
W = 1000/√1000
W = √1000
At this point, we need present the second order differential of the the function of P so as to verify that the perimeter P is minimum for the above calculated dimensions of L and W.
Thus, d²P/dL² = 4000/L³
Since L > 0, we can state d²P/dL² is a positive number. This is an indication that the answers we got for the Perimeter as well as the Length (L) and Width (W) dimensions of the rectangle are the minimum values. That is to say that dimensions of the rectangle covering an area of 1,000 m² has a perimeter which is as small as possible. This goes on to affirm that the rectangle occupying a total area of 1,000 m² is a square of side √1000 m.
Thus, the dimensions of a rectangle with an area 1,000m² whose perimeter is as small as possible is 10√10 and 10√10.
So this is How To Find The Length And Width Of A Rectangle When Given The Perimeter And Area
Find The Dimensions Of A Rectangle With Perimeter 100m Whose Area Is As Large As Possible
The area of any rectangle can be said to be the total region covered by the rectangle while the perimeter is the total distance round a rectangular shape.
The dimensions of the rectangle with a perimeter of 100 m which has an area as large as possible can be calculated below:
Area Of A Rectangle Formula = Length × Width
Perimeter Of A Rectangle = 2 x (Length + Width)
Let ‘A’ be called the area of the rectangle and ‘P’ stands for the perimeter of the rectangle. Also, let ‘x’ be the length of the rectangle and ‘y’ be the width of the rectangle.
But Perimeter Of A Rectangle = 2 x (Length + Width)
So, P = 2 (x + y)
Since the perimeter of the given rectangle is 100 m, we will have that:
100 = 2 (x +y)
Dividing both sides by 2, we have as follows:
x + y = 50
y = 50 – x —————————– (Equation 1)
Also, Area Of A Rectangle = Length × Width
A = xy ——————- (Equation 2)
If we substitute the value of y from equation (1) into equation (2) we will have the following statement:
Area = x (50 – x )
Area A(x) = 50 x – x²
Computing the derivative of A(x) we will have below:
A'(x) = 50 – 2x
Finding the critical points we have the following:
50 – 2x = 0
2x = 50
Therefore x = 25
Now, we need to substitute x = 25 into equation (1) to get the following statement:
y = 50 – x
y = 50 – 25
Thus, y = 25
In conclusion, the rectangle having a maximum area is a square figure with side lengths measuring 25 m each. So this is How To Find The Length And Width Of A Rectangle When Given The Perimeter And Area.
Area Of Rectangle Examples
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- The width of a rectangle is 6 feet, and the diagonal is 10 feet. what is the area of the rectangle?
- If the perimeter of a rectangle is 24 what is the area
- If a 4 × 16 rectangle has the same area as a square, what is the length of a side of the square?
- How To Find The Length And Width Of A Rectangle When Given The Perimeter And Area
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