Question

If the diagonal of a square is decreased by 15% then what is the percentage reduction in the area of the square?

Answer 1

area of square = side×side
and its decrease by 15% by side.
hence, area of square reduce = 4×side
=15%×4 (sides)
= 60%

Answer 2

Let the side of square be a.

Length of diagonal is

$\sqrt{ {a}^{2} + {a}^{2} } = a \sqrt{2}$

When the length of diagonal is decreased by 15%, current length of diagonal be d′=(1−15/100)∗a√2=0.85∗a√2

Let the side of new square be a′

Relation between a′ and d′ is

d′=a′√2

⇒0.85∗a √2=a′√2

⇒a′=0.85a

Area of new square is (a′)² =(0.85a)²=0.7225a²

Percent decrease in area is

$\frac{ {a}^{2} - 0225 {a}^{2} }{ {a}^{2} } \times 100=27.75%$