Question

84. A rectangle is 14 cm long and 10 cm wide. By what %age does the length
change if we convert this into a square of the same area?
a) 10%
b) 20%
c) 15%
d) 12%​

Answer 1

Hope you will understand it.

Answer 2

Answer: 15%

Given,

A rectangle 14 cm long and 10 cm wide.

To find,

Percentage change in length if the given rectangle is converted into a square.

solution,

Area of a rectangle = Length × Breadth

So, the area of the given rectangle = 14cm × 10cm = 140 cm²

Now, this rectangle is converted into a square of the same area:

Area of a square = side × side

Let the side of the square be 'a'

Area of square = a²

140 = a²

√140 = a

11. 83 = a

So, each side of the square formed = 11. 83 cm

Now, to calculate the percentage change in length when the given rectangle is converted into a square of the same area:

Let the Percentage change be X

X = (initial length- final length) ÷ Initial length × 100

X= (14 - 11.83) ÷ 14 × 100

X= 2.17÷ 14 × 100

X= 15.5

Therefore, the percentage change in length when the given rectangle is converted into a square of the same area = 15% (approx).

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