Question

The height of a triangle is four × the length of the base. Find the base and height of the triangle if the area is 18 square inches.

A. Base = 3 inches, Height = 12 inches
B. Base = 4.5 inches, Height = 18 inches
C. Base = 6 inches, Height = 24 inches
D. Base = 9 inches, Height = 36 inches

Answer 1

To solve for the base and height, the area formula A = 1/2 × base × height is used, with the height set as four times the base. Calculating leads to a base of 3 inches and a height of 12 inches, making option A the correct answer.

Step-by-step explanation:

To find the base and height of the triangle with an area of 18 square inches, where the height is four times the length of the base, we use the formula for the area of a triangle A = 1/2 × base × height. Let's denote the base by 'b' and the height as '4b' (since it is four times the base).

Substituting into the area formula we get:

18 = 1/2 × b × (4b)

18 = 2b²

b² = 9

b = 3 inches (since the base can't be negative)

Now, calculating the height:

Height = 4 × base = 4 × 3 = 12 inches

Therefore, the answer is A. Base = 3 inches, Height = 12 inches.