Question

In a right-angled triangle, the square of the hypotenuse is twice the product of the square of the other sides. Then the triangle is:

• A. equilateral
• B. isosceles
• C. of angles ${30}^o,{60}^o,{90}^o$
• D. of angles ${40}^o,{50}^o,{90}^o$

Answer 1

The correct option is B isosceles

Let the three sides of triangle are base $\left(b\right)$, perpendicular $\left(p\right)$ and hypotenuse $\left(h\right)$.

Then according to the given condition, we have

$h^2=2b\times p$

$\Rightarrow b^2+p^2=2b\times p$

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

$\Rightarrow b=p$

So, triangle is an isosceles triangle with angle $={45}^o$.