Question

The area of a triangle is 1,440 cm2. The base of the triangle is 5 times the height. What is the height of the triangle?

Answer 1

The height of the triangle = 24 cm

Explanation:

∵ The area of the triangle = 1/2 × base × height

∵ The length of the base = 5 times the length of the height

Let the length of the height = x, then length of the base = 5x

∴ Area triangle = 1/2 × 5x × x = 2.5 x²

∵ Area of the triangle = 1440 cm²

∴ 2.5 x² = 1440

∴ x² = 1440 ÷ 2.5 = 576

∴ x = √576 = 24 cm

∴ The height of the triangle = 24 cm

Answer 2

Answer: 24 cm

Explanation:

The formula for calculate the area of a triangle is:

`A=bh/2`

Where b is the base and h is the height.

Then if the base of the triangle is 5 times the height:

`b=5h`

Substitute the above into the formula and solve for the height. Therefore, you obtain that the height is:

`1,440=(5h*h)/(2)\\1,440=(5h^(2))/(2)`

`1,440cm^(2)=5h^(2)/2\\h=\sqrt{(2(1,440))/(5)}\\h=24cm`