Question

In a right angled triangle, the square of the hypotenuse is equal to twice the product of the other two sides. One of the acute angles of the triangle is

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

The correct option is B

${45}^{\circ }$

Let the sides be "a” and "b”
c be the hypotenuse

Given that, square of the hypotenuse is equal to twice the product of the other two sides.
By pythogoras theorem,
$c^2=a^2+b^2$
So, $a^2+b^2=2ab$
$a^2+b^2-2ab=0$
$(a-b{)}^2=0$
$a=b$
$\therefore \angle A=\angle B$
$\angle A+\angle B+\angle C={180}^{\circ }$
$2\angle A+90=180$
$\angle A=\angle B={45}^{\circ }$