Question

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

• A. $14cm$
• B. $13cm$
• C. $12cm$
• D. $11cm$

Answer 1

The correct option is B

$13cm$

Correct option: (b) $13cm$

Explanation :

Given smallest side is $5cm$. Let us consider it as base.

We know that,

Area of triangle $=\frac{1}{2}\times base\times height$

$\begin{array}{rcl}& \Rightarrow & 30=\frac{1}{2}\times 5\times height\\ & \Rightarrow & 30\times 2=5\times height\\ & \Rightarrow & 60=5\times height\\ & \Rightarrow & height=\frac{60}{5}=12cm\\ & & \end{array}$

From Pythagoras theorem,

$\begin{array}{rcl}Hypotenus{e}^2& =& heigh{t}^2+bas{e}^2\\ & =& {12}^2+5^2\\ & =& 144+25\\ & =& 169\end{array}$

$\begin{array}{rcl}Hypotenus& =& \sqrt{169}\\ & =& `13cm\end{array}$

Hence, the correct option is (b)