Question

The area of a right angled triangle is $40sq.cm$ and its perimeter is $40cm.$ The length of its hypotenuse is

• A. $16cm$
• B. $18cm$
• C. $17cm$
• D. Data insufficient

Answer 1

The correct option is B $18cm$

$\Delta ABC$ is a right angled triangle.
Area of triangle $ABC=40sq.cm$
$\Rightarrow \frac{1}{2}\times AB\times BC=40$ ...(1)

Perimeter of triangle $ABC=40cm$
$\Rightarrow AB+BC+CA=40$ ...(2)

Also, by Pythagoras theorem
$A{C}^2=A{B}^2+B{C}^2$ ....(3)
From (2), $AB+BC=40-AC$
Squaring both the sides, we get
$(AB+BC{)}^2=(40-AC{)}^2$
$\Rightarrow A{B}^2+B{C}^2+2AB.BC=1600+A{C}^2-2\times 40\times AC$
$\Rightarrow A{C}^2+2\times 80=1600+A{C}^2-80AC$ (from 1 and 3)
$\Rightarrow 160=1600-80AC$
$\Rightarrow AC=18cm$

Hence, the hypotenuse is $18cm$.