Question

Two lawns have the same area, 121 sq m. One is a square, and the other is rectangular, and four times the perimeter of the rectangle is equal to five times that of the square. The length and breadth of the rectangle are:

(a) 11m, 11m

(b) 22 m, \(5\frac 12\) m

(c) 55 m, \(2\frac 15\) m

(d) 33 m, \(3\frac 23\) m

Answer 1

Correct option is (b) 22 m, \(5\frac 12\) m

Let the side of the square be x.

Hence, x² = 121

∴ x = ±11

Hence, side length of the square is 11 m.

Now let l and b be the length and breadth of the rectangle.

Hence, 4(2(l + b)) = 5(4 × 11)

2(l + b) = 55

l = \(\frac{55}2\) − b

And Area is = 121 = l.b

= \(b\left(\frac{55}2 - b\right)\)

∴ 55b − 2b² = 242

2b² − 55b + 242 = 0

b = 22m and b = \(\frac{11}2\) m

If b = 22m then

l = \(\frac{55 - 44}2\)

= \( \frac{11}2\) m or \(5\frac 12\) m