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

Answer:

D. 4in, 12in

Step-by-step explanation:

Area of triangle  = 24in²

Unknown:

Base and height of the triangle = ?

Solution:

The area of a triangle  = $\frac{1}{2}$ x base x height

   From the problem,

        base  = $\frac{1}{3}$ x height

let the base  = b

            height  = h

         b =  $\frac{1}{3}$h

          h = 3b

Input into the formula of area;

       24  =  $\frac{1}{2}$ x b x 3b

   Mulitply through by 2;

       48 = 3b²

         b² = 16

         b = √16 = 4

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