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 m2MathematicsRD Sharma (2019, 2020)All

Suggest Corrections

0

Similar questions
View More

Same exercise questions
View More