Question

kyla makes a triangular school pennant. the area of the triangle is 180 square inches. the base of the pennant is z inches long. the height is 6 inches longer than twice the base length. what is the height of the pennant? recall the formula a = \frac{1}{2}bh. \bigcirc 12 inches \bigcirc 15 inches \bigcirc 30 inches \bigcirc 36 inches image of a triangular pennant with base z in. and height (2z + 6) in., labeled terrell high school, go, hornets!

Explanation:

Step1: Identify given values

Base \( b = z \), height \( h = 2z + 6 \), area \( A = 180 \). Formula: \( A=\frac{1}{2}bh \).

Step2: Substitute into formula

\( 180=\frac{1}{2}(z)(2z + 6) \)
Simplify: \( 180=\frac{1}{2}(2z^2 + 6z) \) → \( 180 = z^2 + 3z \)

Step3: Solve quadratic equation

\( z^2 + 3z - 180 = 0 \)
Factor: \( (z + 15)(z - 12) = 0 \)
Solutions: \( z = -15 \) (discard, length can't be negative) or \( z = 12 \)

Step4: Find height

Height \( h = 2z + 6 = 2(12) + 6 = 30 \) inches.

Answer:

30 inches (Option: 30 inches)