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.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

7 weeks

step-by-step explanation:

convert each fraction to the least common multiple of 20, so 3/4 = 15/20 & 1/10 = 2/20, then divide 15 by 2 and you get a little over 7, so the food will last 7 weeks.