Incline mats, or triangle mats, are offered with different levels of incline to help gymnasts learn basic moves. As the name may suggest, two sides of the mat are right triangles. If the height of the mat is 35 inches shorter than the length of the mat and the hypotenuse is 5 inches longer than the length of the mat, what is the length of the mat?

Hypotenuse = 65

Height = 25

Length = 60

Step-by-step explanation:

Let's assume that the mat is a right triangle Taking length of triangle to be P

so height = p-35 (35 inches shorter)

hypotenuse = p+5 (5 inches longer)

for right triangle. Therefore, we would apply Pythagoras theorem;

so (p+5)² = p²+(p-35)² by expansion we get p²+ 10p+ 25 = p²+p²- 70p+1225

-P²+80p-1200 = 0

P²-80p+1200 = 0

Solving for p quadratically we'll get

P = 60 or P = 20

So the length of the mat would be

60 and height = 60-35 = 25

Hypotenuse = 60+5 = 65

We chose 60 because using 20 would make height to be negative.

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