In the right triangle, find the length (in inches) of the altitude drawn to the hypotenuse. Use the fact that the area of the polygon is unique.

Question

In the right triangle, find the length (in inches) of the altitude drawn to the hypotenuse. Use the fact that the area of the polygon is unique.

A right triangle has a shorter leg labeled 7 inches and a longer leg labeled 24 inches. A line segment inside the triangle connects the vertex of the right angle to the hypotenuse, forming a right angle with the hypotenuse.

Answer 1

area = half base times height

A=bh/2

area = (7 x 24)/2 = 168/2 = 84

hypotenuse = square root of (49+ 576) = sqr625 = 25

area = 84 = bh/2 = 25h/2

25h = 2(84) = 168

h= 168/25 = 6.72 inches