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

Explanation:

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

A =
`(1)/(2)`bh

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

2b = 5h , that is

b =
`(5h)/(2)`

Substitute this into the formula for finding area , that is

80 =
`(1)/(2)` X
`(5h)/(2)` X h

80 =
`(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 =
`(5h)/(2)` , then

b = 20 inches

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