Question

The base and hypotenuse of a right triangle are respectively 5cm and 13cm long. Its area is

• A. $25c{m}^2$
• B. $28c{m}^2$
• C. $30c{m}^2$
• D. $40c{m}^2$

Answer 1

The correct option is C

$30c{m}^2$

In a right triangle base = 5 cm base hypotenuse = 13 cm
But $A{B}^2+B{C}^2=A{C}^2$ (Pythagoras Theorem)
$\Rightarrow A{B}^2+(5{)}^2=(13{)}^2\Rightarrow A{B}^2+25=169$
$A{B}^2=169-25=144=(12{)}^2$
$\therefore AB=12cm$
Now area = $\frac{1}{2}base\times altitude$
=$\frac{1}{2}\times 5\times 12=30c{m}^2$