Question

the height of a triangle is 4x inches and the base is (5x+1) inches. the area of the triangle is 500 square inches. what are the dimensions of the base and height of the triangle?

Answer 1

Height = 28 inches, Base = 36 inches

Explanation:

Height of a triangle is 4x inches and the base is (5x+1) inches.

Area of the triangle is given as 500 square inches.

We have to calculate the dimensions of the triangle.

Since area of a triangle = (1/2)×Base×height = 500

(1/2)×(4x)×(5x+1) = 500

2x(5x+1) = 500

x(5x+1) = 250

5x² + x - 250 = 0

`x=(-1\pm √(1+20* 250))/(2* 5)`

`=(-1\pm √(5001))/(10)=(-1\pm 70.72)/(10)`

x = 7

Therefore height = 4x = 28 inches

Base = (5x + 1) = 35+1 = 36 inches.