Question

8. If the side of a square is increased
by 25%, then its area is increased
by :​

Answer 1

Step-by-step explanation:

Let the side of square to be x

Then the area =X2

As per problem

The side of square is increased by 25% = 25%×x

=25/100×x

=x/4

The new area =(x/4)2

=X2/16

Answer 2

$\underbrace \text{Answer:-}$

Let the side of the square be a.

Then, area= a²

$\tt{Increased \: side:a + a \times \frac{25}{100} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \tt{ \frac{5a}{4} }$

$\rm{Area: \frac{5a}{4} \times \frac{5a}{4} } = \frac{25 {a}^{2} }{16}$

Increased in area: 25a²/16-a² = 9a²/16

$\sf{Increased\%: \frac{ 9 {a}^{2} }{16 \times {a}^{2} } \times 100}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \tt{ \frac{ {9a}^{2} }{ \cancel{16}} \times \frac{1}{ {a}^{2} } \times \cancel{100}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \tt{\frac{9 \times 25}{4} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \bf \red{56.25\%}$