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 = 1/2bh.
a.) 12 inches
b.) 15 inches
c.) 30 inches
d.) 36 inches

A = 1/2 * b * h
A = 180
b = z
h = 2z + 6

180 = 1/2 * z * 2z + 6
180 = (2z^2 + 6z)/ 2
180 = z^2 + 3z)
z^2 + 3z - 180 = 0
(z - 12)(z + 15) = 0

z - 12 = 0
z = 12

z + 15 = 0
z = -15not this one because it is negative

h = 2z + 6
h = 2(12) + 6
h = 24 + 6
h = 30 inches <

The formula for area of a triangle = BH / 2
In which the area = 180 square inches.

You can therefore make this formula:

180 = [2(2z+6)+6](2z+6) / 2

Now solve for z.

360 = [2(2z+6)+6](2z+6)
360 = (4z+12+6)(2z+6)
360 = (4z+18)(2z+6)
360 = 8z^2 + 24z + 36z + 108
360 = 8z^2 + 60z + 108
    0 = 8z^2 + 60z - 252

Now we will use quadratic formula to get z = 3, -21/2

Substitute in now

2(2z+6) + 6
2(2(3)+6) + 6
2(6+6) + 6
2(12) + 6
24 + 6
30

or... (false)

2[2(-10.5)+6]+6
2(-21+6)+6
2(-15) + 6
-30 + 6
-24

Therefore, the height is 30 inches. I made some work errors but it is still true because of the property ab = ba

The lateral side of a triangular pyramid is a triangle. in order to increase the lateral surface area, the slant height and the height should be altered