Questions: Recall that the area of a triangle is A=1/2 B * H, where B is the base and H is the height. The base of a triangle is 4 times the height. If the area is 392 square feet, then what is the height of the triangle, in feet?

Solution Steps

To find the height of the triangle, we can use the formula for the area of a triangle \( A = \frac{1}{2} B \cdot H \). Given that the base \( B \) is 4 times the height \( H \), we can express the base as \( B = 4H \). Substitute this into the area formula and solve for \( H \).

The area \( A \) of a triangle is given by the formula: \[ A = \frac{1}{2} B \cdot H \] where \( B \) is the base and \( H \) is the height.

We know that the base \( B \) is 4 times the height \( H \): \[ B = 4H \]

Substituting \( B \) into the area formula gives: \[ A = \frac{1}{2} (4H) H = 2H^2 \] Setting the area \( A \) to 392 square feet, we have: \[ 2H^2 = 392 \] Dividing both sides by 2: \[ H^2 = 196 \] Taking the square root of both sides: \[ H = \sqrt{196} = 14 \]

Final Answer