Question

Chelsea is making a kite in the shape of a triangle. To determine if the triangle is a right triangle, Chelsea completed the following steps.
Step 1:
Find the side lengths of the triangle: 30 inches, 24 inches, 18 inches.

Step 2:
Substitute the values into the Pythagorean theorem: 18 squared + 24 squared = 30 squared.

Step 3:
Combine like terms: (18 + 24) squared = 30 squared.

Step 4:
Evaluate each side: 1764 not-equals 900.

Chelsea says the triangle is not a right triangle. Which best describes the accuracy of her explanation?

Answer 1

She made a mistake on step 3

The $18^2+24^2$ is not the same as $(18+24)^2$

This is what her steps should look like

$a^2 + b^2 = c^2\\\\18^2 + 24^2 = 30^2\\\\324 + 576 = 900\\\\900 = 900$

Since we get the same number on both sides, this means the last equation is true. This means the first equation is also true. Therefore, she does have a right triangle. Refer to the converse of the pythagorean theorem for more info.