Question

Question 18

Area of a right angled triangle is $30c{m}^2$. If its smallest side is 5 cm, then its hypotenuse is

(a) 14 cm
(b) 13 cm
(c) 12 cm
(d) 11 cm

Answer 1

Given, area of right angled triangle = $30c{m}^2$
And smallest side i.e. base = 5 cm
We know that,
Area of right angled triangle $=\frac{1}{2}\times Base\times Height$
$\therefore 30=\frac{1}{2}\times 5\times Height$
$\Rightarrow Height=\frac{30\times 2}{5}$
$\Rightarrow Height=12cm$
Now, according to Pthagoras theorem,
$(Hypotenuse{)}^2=(Perpendicular{)}^2+(Base{)}^2$
$\Rightarrow (Hypotenuse{)}^2=(12{)}^2+(5{)}^2$ $[\because height=perpendicular]$
$\Rightarrow (Hypotenuse{)}^2=144+25$
$\Rightarrow (Hypotenuse{)}^2=169$
$\Rightarrow Hypotenuse=\sqrt{169}$
$\Rightarrow Hypotenuse=13cm$