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.

a net is a diagram that shows a “flattened” view of a solid. in a net, each face and base is shown with all of its dimensions. a net can also serve as a pattern to build a three-dimensional solid.

a pyramid is a three-dimensional object with a base that is a polygon and triangular faces that meet at one vertex.

" the net of a triangular pyramid consists of four triangles. the base here we are given of the pyramid is a equilateral   triangle, and the lateral faces are also triangles "

answer: the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

step-by-step explanation:

the given rate of interest i= 85%

in calculating the monthly payment for a loan with an interest rate compounded monthly, the value of the interest rate per period we use in the formula must be in decimal form.

to convert it in decimal, we divide it by 100, we get

hence, the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.