Incline mats, or triangle mats, are offered with different levels of incline to gymnasts learn basic moves. as the name may suggest, two sides of the mat are right triangles. if the height of the mat is 21 inches shorter than the length of the mat and the hypotenuse is 6 inches longer than the length of the mat, what is the length of the mat?

Let's assume the mat as a right triangle Taking length of triangle be x so height = x-21 and hypotenuse= x+6 for right triangle we can apply pythagoras theorem so (x+6)^2=x^2+(x-21)^2 expanding we get x^2 + 12 x + 36 = 2 x^2 - 42 x + 441 solving for x we get x=9,45 But for length to be 9 height will be negative So the length of mat will be 45 inches