Question

find the side labeled x. (assume a = 32). x =

Explanation:

Step1: Identify triangle type

The triangle is a right - isosceles triangle since one angle is 90° and another is 45°. In a right - isosceles triangle, the two legs are equal. Here, side $a$ is a leg and side $x$ is the hypotenuse.

Step2: Apply Pythagorean theorem

For a right - triangle with legs of length $a$ and $a$ and hypotenuse $x$, by the Pythagorean theorem $x^{2}=a^{2}+a^{2}=2a^{2}$. Given $a = 32$, then $x^{2}=2\times32^{2}$.

Step3: Solve for $x$

$x=\sqrt{2\times32^{2}}=\sqrt{2}\times32$.

Answer:

$32\sqrt{2}$