Question

Jordan measures the side lengths of a triangular piece of sheet metal. The side lengths are 156 cm, 133cm, and 205 cm. Verify that the triangular piece of sheet metal is a right triangle. (this problem involves polynomial identities)

Please help as soon as possible, thank you!!

Answer 1

see the explanation

Explanation:

we know that

If the triangular piece of sheet metal is a right triangle, then the side lengths must satisfy the Pythagorean Theorem

so

`c^2=a^2+b^2`

where

c is the hypotenuse (the greater side)

a and b are the legs of triangle

we have

`c=205\ cm\\a=156\ cm\\b=133\ cm`

substitute

`205^2=156^2+133^2`

`42,025=24,336+17,689`

`42,025=42,025` ----> is true

so

The side lengths satisfy the Pythagorean Theorem

therefore

The triangular piece of sheet metal is a right triangle