Question

The length of a rectangle is twenty five percent more than its breadth. The area of the
rectangle is 1620 sq cm. What is the area of a square whose side is half the length of the
rectangle?
a.506.25 sq cm B. 512.75 sq cm c. 515.25 sq cm d. 509.75 sq cm e. None of these
bobo

Answer 1

We know that the Area of a rectangle is the product of length and breadth, Thus.,

♦ Area A of rectangular plot = L × B....... equation 1

• Let the breadth of the rectangle be 'x'

According to the question,

That is, length = Breadth + (25/100) breadth

put breadth as 'x'

$x + ( \frac{25}{100} )x \\ breadth + 0.25 \times breadth \: \: \: \: ie \: x + (0.25 \times x) \\ \: area = 1.25x \times x = 1.25 {x}^{2}$

Given, A = 1620 sq cm.

1620 = 1.25 x²

1620 / 1.25 = x²

• 1296 = x² ( square metre)

Taking square root for both side,

x = 36

i.e. Breadth = 36

Let's find length from breadth,

L = x + ( 25/100) × x

L = 36 + (0.25 × 36)

L = 36 + 9

L = 45

So from this we get length of rectangle which is 45,

we know that, length of square is half of the length of rectangle, according to this

Length of each side of Square = Length of the rectangle / 2

= 45 / 2

= 22.5

Area of Square = L²

= 22.5 × 22.5

= 506.25 sq cm.

So The correct option no. is a) 506.25 sq cm