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 28 inches shorter than the length of the mat and the hypotenuse is 8 inches longer than the length of the mat, what is the length of the mat?

Answer:The length of the mat is 60 in.Step-by-step explanation:Given :Mats are inclined to form a triangle.two sides of the mat are right triangles.Hence the triangle formed is right angled triangle.Let the length  be x.Now,The height of the mat is 28 inches shorter than the length of the mat.Height of mat = x - 28Also, the hypotenuse is 8 inches longer than the length of the mat.Hypotenuse = x + 8Hence by using Pythagoras theorem we get ,[tex]Hypotenuse^2= lenght^2+height^2\\[/tex][tex]x^2+(x-28)^2=(x+8)^2\\x^2+x^2-56x+784=x^2+16x+64\\x^2-72x+720=0\\x^2-60x-12x+720 = 0\\x(x-60)-12(x-60)=0\\(x-12)(x-60) = 0\\x-12=0\\x=12\\x-60=0\\x=60[/tex]Now we get 2 values of length 12 and 60.But height is 28 in less than length.And when we take length value as 12 the height will be negative hence it can't be true.Hence the Length of mat = 60 in.