Question

In a right angle triangle if the square of hypotenuse is equal to twice the product of the other two sides, then one of the acute angle of the triangle is:

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

Answer 1

Answer: (B)

${45}^{\circ }$

Given, $△ABC$, right angled at $B$.
$A{C}^2=2AB.BC$
Also, by Pythagoras theorem,
$A{C}^2=A{B}^2+B{C}^2$
$2AB.BC=A{B}^2+B{C}^2$
$A{B}^2+B{C}^2-2AB.BC=0$
$(AB-BC{)}^2=0$
$AB=BC$
Thus, $\angle BAC=\angle BCA$ ........... (Isosceles triangle property)
$\angle BAC=\angle BCA=\frac{{180}^{\circ }-\angle B}{2}$
$\Rightarrow \angle BAC=\angle BCA={45}^{\circ }$