Question

Jorge wants to prove that a triangle with sides of length 7, 10, and x is a right triangle, where x<10 .

Complete the sentence below by dragging and dropping the correct values into the boxes.
Jorge must show that _____ and _____ have the same value.

Answer 1

• x² + 7²
• 10²

Explanation:

Joey wants the relation between 7, 10, and x that will show a triangle with sides 7, 10, and x is a right triangle, where x < 10.

Right triangle

There are two features of a right triangle that are of interest here.

1. the legs are shorter than the hypotenuse
2. the Pythagorean theorem is satisfied.

Since the side with measure x is less than 10, the side of length 10 is the longest, hence the hypotenuse.

Pythagorean theorem

The Pythagorean theorem tells us the sum of the squares of the legs is equal to the square of the hypotenuse for a right triangle. Showing this condition is met is sufficient to show that the triangle is a right triangle.

For legs x and 7, and hypotenuse 10, this is ...

x² + 7² = 10²

Jorge must show that x² + 7² and 10² have the same value.