Question

The area of a triangle is 80in^2. The ratio of the length of its base to its height is 5:2. What are the base and height of the triangle? ..... show work

Answer 1

Answer: base = 20 inches , height = 8 inches

Step-by-step explanation:

The formula fro calculating the area of  a triangle , given the base and the height is given as ;

A = $\frac{1}{2}$bh

The ratio of its base to the height is given as 5: 2 , this means that

2b = 5h , that is

b = $\frac{5h}{2}$

Substitute this into the formula for finding area , that is

80 = $\frac{1}{2}$ X $\frac{5h}{2}$ X h

80 = $\frac{5h^{2}}{4}$

Therefore :

$5h^{2}$ = 80 x 4

$5h^{2}$ = 320

$h^{2}$ = 320 / 5

$5h^{2}$ = 64

h = 8 inches

Substitute h = 8 into b = $\frac{5h}{2}$ , then

b = 20 inches

Therefore , the base of the triangle is 20 inches and the height is 8 inches