Question

the triangular gable on this structure is 16 feet tall. the area of the gable is 192 ft². what is the length of the base?

Explanation:

Step1: Recall triangle area formula

The area \( A \) of a triangle is given by \( A = \frac{1}{2} \times \text{base} \times \text{height} \). Let the base be \( b \) and height \( h = 16 \) ft, area \( A = 192 \) \( \text{ft}^2 \).

Step2: Substitute values into formula

Substitute \( A = 192 \), \( h = 16 \) into \( A = \frac{1}{2} \times b \times h \):
\( 192 = \frac{1}{2} \times b \times 16 \)

Step3: Solve for base \( b \)

Simplify the right - hand side: \( \frac{1}{2} \times 16\times b=8b \). So the equation becomes \( 192 = 8b \).
Divide both sides by 8: \( b=\frac{192}{8}=24 \).

Answer:

The length of the base is 24 feet.