Question

In a right triangle ABC right angled at B, the square of hypotenuse is equal to twice the product of the perpendicular sides. Find the measure of $\angle A.$

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${45}^{\circ }$
• D. Can't be found

Answer 1

The correct option is C

${45}^{\circ }$

In any right angled triangle,

$p^2+b^2=h^2$ [Pythagoras theorem]---(I)

Given: $h^2=2pb$

Putting the value of $h^2$ in (I)

$p^2+b^2=2pb$

$\Rightarrow p^2+b^2-2pb=0$

$\Rightarrow (p-b{)}^2=0$

$\Rightarrow (p-b)=0$

$\Rightarrow p=b$

So, it is an isosceles right angled triangle.

Hence, $\angle A={45}^{\circ }$