Question

The sum of the areas of two squares is $325c{m}^2$ . The side of the larger square is $5cm$ longer than the side of the smaller square. Find the side of each square.

Answer 1

Let the side of square (1) = $s_1$

The side of $2^{nd}$ square = a

Acc to Ques :

$s=5+a$ _ (1)

and $s^2+a^2=325$ _ (2)

so, $(5+a{)}^2+a^2=325$

$25+a^2+10a+a^2=325$

$2a^2+10a=300$

$2a^2+10a-300=0$

$a^2+15a-5a-150=0$

$(a+15)(a-5)=0$

$\therefore a=5$

and $s=10$

$\therefore$ side of smaller square = 5 cm

side of larger square = 10 cm