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 = bh.

Answer 1

Answer:

Height of the pennant is 30 inches.

Step-by-step explanation:

Given that:

Area of pennant = 180 sq inches

Base of pennant = z inches

Height of pennant = (2z + 6) inches

Also, it is a triangular pennant and area of a triangle can be given as:

$A = \dfrac{1}{2} \times Base\times Height$

Putting the values in above formula:

$180 = \dfrac{1}{2} \times z \times (2z+6)\\\Rightarrow 360 = 2z^{2} + 6z\\\Rightarrow 180 = z^{2} + 3z\\\Rightarrow z^{2} + 3z -180 = 0\\\Rightarrow z^{2} + 15z -12z -180 = 0\\\Rightarrow z(z + 15) -12(z+15) = 0\\\Rightarrow (z + 15) (z-12) = 0\\\Rightarrow z = 12\ or\ z=-15$

Value of z can not be negative, so value of Base, z = 12 inches.

Height is given as 2z + 6 so, height = 2$\times$12 +6 = 30 inches