Question

The areas of the squares adjacent to two sides of a right triangle are shown below.

Answer 1

Answer:

$85\:\mathrm{units^2}$

Step-by-step explanation:

All side lengths of a square are equal. The three squares create a right triangle, and the hypotenuse of this triangle represents the side length of the square.

All right triangles must follow the Pythagorean Theorem $a^2+b^2=c^2$ where $c$ is the hypotenuse of the triangle.

Therefore, let $h$ be the side length of this largest square. Since the area of a square with side length $s$ is given by $s^2$, $h^2$ will represent the area of the square:

$\sqrt{35}^2+\sqrt{50}^2=h^2=\boxed{85\:\mathrm{units^2}}$