Question

If the perimeter of the right triangle is 40 mm and the area 120 mm^2, the length of
the hypotenuse is:​

Answer 1

Answer:

length of the hypotenuse = 14 mm

Step-by-step explanation:

Let x = 1/hypotenuse; and t = angle between the base and the hypotenuse; unit: mm.

Area = sin(t)/x * cos(t)/x * (1/2) = 120 → sin(t) * cos(t) = 240 * x^2. … Eq(1).

Perimeter = (1 + cos(t) + sin(t))/x = 40 → cos(t) + sin(t) = 40x - 1.

Square both sides: 2*sin(t)*cos(t) + 1 = 1600x^2 - 80x + 1 →

sin(t)*cos(t) = 800x^2 - 40x. Compare with Eq(1) and ignore the solution x = 0.

x = 1/14 → hypotenuse = 14 mm.