Question

A right triangle's height is 3 times the length of its base. if the area of the triangle is 864, what is the height?

Answer 1

The area of a triangle is a half times base times height.

A = 0.5bh

864 = (0.5)(b)(3b)

864 = 0.5 × 3b^2

1728 = 3b^2

576 = b^2

√576 = √b^2

24 = b

Since the triangle's height is 3 times the length of its base then, the height is 72.

If we check the area by multiplying all values..

A = 0.5bh

864 = (0.5)(24)(72)

864 = 864

The height of 72 is the correct value

Answer 2

Based on the calculations, the height of the triangle is 72 units.

• Let the height of the triangle be h.

• Let the base of the triangle be b.

Given the following data:

• Area of triangle = 864 units.

How to calculate the height.

Translating the word problem into an algebraic expression, we have;

The height is 3 times the length of its base:

$h=3b$

The area of a triangle.

Mathematically, the area of the triangle is given by the formula:

$Area=\frac{1}{2} \times base \times height$

Substituting the given parameters into the formula, we have;

$864=\frac{1}{2} \times b \times 3b\\\\864=\frac{1}{2} \times 3b^2\\\\1728=3b^2\\\\b^2=576\\\\b=\sqrt{576}$

Base = 24 units.

For the height:

$h=3b\\\\h=3 \times 24$

Height, h = 72 units.

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