Question

A triangle has side lengths of 3x,4x and 5x. If the area of the triangle is 121.5cm2, use any appropriate method to determine the value of x.

Answer 1

Answer: x = 4.5

Work Shown:

The 3-4-5 right triangle is the classic pythagorean triple. Scaling each side by x will mean the triangle remains a right triangle.

The longest side is 5x which is the hypotenuse. The two legs are perpendicular to each other. They form the base and height in either order.

base = 3x

height = 4x

area = 0.5*base*height

121.5 = 0.5*3x*4x

6x^2 = 121.5

x^2 = 121.5/6

x^2 = 20.25

x = sqrt(20.25)

x = 4.5