SOLUTION: Hi, I need help with this problem, mainly just how to come up with an equation to use in the Quadratic Formula. Thanks! The Garys have a triangular pennant of area 420 in^2 flyi

Question 433239: Hi, I need help with this problem, mainly just how to come up with an equation to use in the Quadratic Formula. Thanks!
The Garys have a triangular pennant of area 420 in^2 flying from the flagpole in their yard. the height of the triangle is 10in less than 5 times the base of the triangle. What are the dimensions of the pennant?
Found 2 solutions by scott8148, nerdybill:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
420 = (1/2)(b)(h)

420 = (1/2)(b)(5b-10)

840 = 5b^2 - 10b

0 = b^2 - 2b - 168
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
The Garys have a triangular pennant of area 420 in^2 flying from the flagpole in their yard. the height of the triangle is 10in less than 5 times the base of the triangle. What are the dimensions of the pennant?
.
We know that for ANY triangle:
area = (1/2)bh
where
b is length of the base
h is length of the height
.
Let b = base of triangle
then from "the height of the triangle is 10in less than 5 times the base" we get
5b-10 = height
.
our equation:
420 = (1/2)b(5b-10)
840 = b(5b-10)
840 = 5b^2 - 10b
0 = 5b^2 - 10b - 840
0 = b^2 - 2b - 168
0 = (b+12)(b-14)
b = {-12, 14}
We can throw out the negative solution leaving:
b = 14 inches (base)
.
height then:
5b-10 = 5(14)-10 = 70-10 = 60 inches

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