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

C.30 inches

Explanation:

Answer 2

Height of the pennant is 30 inches.

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 = (1)/(2) * Base* Height`

Putting the values in above formula:

`180 = (1)/(2) * z * (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
`*`12 +6 = 30 inches