Question

The area a of right angled triangle is 30 $c{m}^2$ and the length of its hypotenuse is 13 cm . The length of the shorter is:

Answer 1

area of $△=30c{m}^2$

$\frac{1}{2}\times b\times h=30$

$b\times h=60$___(1)

hypotenuse = 13

$\therefore b^2+h^2={13}^2$

$b^2+h^2=169$____(2)

multiplying (1) by 2 and adding to (2)

$b^2+b^2+2bh=169+120$

$(b+h{)}^2=289$

$b+h=17$___(3)

from (1)

$b=\frac{60}{b}$ putting in (3)

$\frac{60}{h}+h=17$

$h^2-17+60=0$

$(h-5)(h-12)=0$

$h=5,12$

shorter is $5cm$