Question

6. Use the Pythagorean theorem to verify right triangles and find the missing lengths.

Part I: Determine if a triangle with the following side measures could be a right triangle:
5, 8, 11
Step 1: Use the Pythagorean Theorem, a² + b²c², and substitute 5 for a, 8 for band 11 for c.
(2 points)
Step 2: Simplify the equation by squaring each value and adding the left side. (3 points)
Step 3: Determine if a triangle with side lengths 5, 8 and 11 is a right triangle. Explain your
answer. (1 point)
Part II: Using the Pythagorean Theorem stated in Part I, find the measure of the hypotenuse c
of the right triangle below. Show your work. (4 points)
10 in,
24 in

Answer 1

See below.

Explanation:

6.

Part I

Step 1

5, 8, 11

Since 11 is the greatest length, if a right triangle with side lengths 5, 8, 11 does exist, then 5 and 8 are the legs and 11 is the hypotenuse.

a² + b² = c²

5² + 8² = 11²

Step 2

25 + 64 = 121

89 = 121

Step 3

89 = 121 is a false statement, so the side lengths 5, 8, 11 cannot form a right triangle.

Part II

10 in. and 24 in. are lengths of the two legs of a right triangle.

We now use the Pythagorean Theorem to find the length of the hypotenuse.

a² + b² = c²

10² + 24² = c²

100 + 576 = c²

c² = 676

c = √676

c = 26

The hypotenuse measures 26 in.