Question

what is the missing side length? first, find the area of the two larger squares and use them to find the area of the smallest square. input the areas. then click done. the image shows a right triangle with hypotenuse 17, one leg 15, and the other leg x. there are three squares: one with side 17 (area a = ?), one with side 15 (area a = ?), and one with side x (area a = ?).

Explanation:

Step1: Identify triangle type

This is a right triangle, so the Pythagorean theorem applies: for legs $a,b$ and hypotenuse $c$, $a^2 + b^2 = c^2$. Here, the squares' areas equal the squares of the triangle's sides.

Step2: Calculate largest square area

Largest square corresponds to hypotenuse 17:
$Area_1 = 17^2 = 289$

Step3: Calculate medium square area

Medium square corresponds to leg 15:
$Area_2 = 15^2 = 225$

Step4: Calculate smallest square area

Use Pythagorean theorem to find $x^2$ (smallest square area):
$x^2 = 17^2 - 15^2 = 289 - 225 = 64$

Answer:

Largest square area: 289
Medium square area: 225
Smallest square area: 64
Missing side length $x$: 8