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Question

The area of a square field is 5184 cm2. A rectangular field, whose length is twice its breadth has its perimeter equal to the perimeter of the square field. Find the area of the rectangular field.


Solution

First, we have to find the perimeter of the square.
The area of the square is r2, where r is the side of the square.
Then, we have the equation as follows:
r2 = 5184 = (2 x 2) x (2 x 2) x (2 x 2) x (3 x 3) x (3 x 3)
Taking the square root, we get r = 2 x 2 x 2 x 3 x 3 = 72
Hence the perimeter of the square is 4 x r = 288 m

Now let L be the length of the rectangular field.
Let W be the width of the rectangular field.
The perimeter is equal to the perimeter of square. 
Hence, we have:
2(L + W) = 288
Moreover, since the length is twice the width:
L = 2 x W.
Substituting this in the previous equation, we get:
2 x (2 x W + W) = 288
               3 x W = 144
                     W = 48
To find L:
L = 2 x W = 2 x 48 = 96
∴ Area of the rectangular field = L x W = 96 x 48 = 4608 m2

Mathematics
RD Sharma (2019, 2020)
All

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