SOLUTION: A triangle has sides with lengths of 4 centimeters, 9 centimeters, and 12 centimeters. Is it a right triangle?

Question 1176696: A triangle has sides with lengths of 4 centimeters, 9 centimeters, and 12 centimeters. Is it a right triangle?

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Rule: If we have a triangle of sides a,b,c such that c is the longest side and a^2+b^2 = c^2 is a true equation, then this triangle is a right triangle. This is the converse of the pythagorean theorem. The regular version of the pythagorean theorem is the reverse (which says if we had a right triangle then a^2+b^2 = c^2 is true)

We have
a = 4
b = 9
c = 12
The order of a,b doesn't matter. So we could have a = 9 and b = 4. Usually 'a' is the smallest of the trio. All that matters is that c is the largest value.

Plug those values into the equation mentioned
a^2 + b^2 = c^2
4^2 + 9^2 = 12^2
16 + 81 = 144
97 = 144
The last equation is false, so the first equation must also be false when (a,b,c) = (4,9,12)

Answer: This is not a right triangle.

RELATED QUESTIONS
A triangle has sides with lengths of 33�centimeters, 56�centimeters, and 65�centimeters.... (answered by rothauserc)

A triangle has side lengths of 9 centimeters, 12 centimeters, and 7 centimeters. Is this... (answered by richard1234)

find the area of a right triangle whose sides have lengths x centimeters, (3x+3)... (answered by josgarithmetic)

A triangle has two sides that have lengths of 12 centimeters and 19 centimeters. Which of (answered by Alan3354)

I don't know how to solve this. The lengths of three sides of a triangle ABC are 6... (answered by vleith)

A triangle has two sides of lengths 4 centimeters and 6 centimeters. Its area is N... (answered by Edwin McCravy)

The legs of a right triangle differ by 2 centimeters and the hypotenuse is 4 centimeters... (answered by jojo14344)

The measures of the legs of a right triangle are 6 centimeters and 9 centimeters. In... (answered by ewatrrr)

Find the lengths of the sides of a right triangle if the hypotenuse is 9 centimeters... (answered by ikleyn)