Question

The base of a triangle is one third of its height. If the area of the triangle is 24 square inches, what are the base and height of the triangle?

A. 3in, 9 in
B. 8in, 24 in
C. 2in, 6in
D. 4in, 12in

Answer 1

D. 4in, 12in

Explanation:

Area of triangle = 24in²

Unknown:

Base and height of the triangle = ?

Solution:

The area of a triangle =
`(1)/(2)` x base x height

From the problem,

base =
`(1)/(3)` x height

let the base = b

height = h

b =
`(1)/(3)`h

h = 3b

Input into the formula of area;

24 =
`(1)/(2)` x b x 3b

Mulitply through by 2;

48 = 3b²

b² = 16

b = √16 = 4

So, h = 3b= 3 x 4 = 12in