Question

A triangle with a base of 8 meters has an area of 60 meters. The longest side of the triangle is 17 meters. Is the triangle a right triangle? Explain

Answer 1

Yes: this situation represents a right triangle.

Explanation:

It's best to draw a picture of this situation. Draw the 8-meter base. If the longest side is 17 meters, this either is or is not the hypotenuse of a right triangle. Given that the area is 60 m^2, write out A = 60 m^2 = (1/2)(base)(height). Alternatively, this is 120 m^2 = (1/2)(base)(height), or 120 m^2 = (8 m)(height. Therefore, the height is

120 m^2

------------- = 15 m

8 m

Then we know for certain that base = 8 m, height = 15 m and (longest side) = 17 m. Apply the Pythagorean Theorem:

8^2 + 15^2 = 17^2 ?? 64 + 225 = 289 ?? YES

Yes, the information given shows that this is a right triangle.