SOLUTION: I need help with this problem: The area of a triange is 90 square feet. The height is 2 less than twice the base. Find the base and height of the triangle. So, A=90 sq ft

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Question 21164: I need help with this problem:
The area of a triange is 90 square feet. The height is 2 less than twice the base. Find the base and height of the triangle.
So, A=90 sq ft and the area of a triangle is 1/2 x B x H. The height of my triangle is going to be 2b-2. Here's where the problem is...I don't know what to do next or how to find what my base is. Any help will be great. Thanks!!
Jenny
Answer by bonster(299) About Me  (Show Source):
You can put this solution on YOUR website!
The area of a triange is 90 square feet. The height is 2 less than twice the base. Find the base and height of the triangle.

A=1%2F2bh
A=90
h=2 less than twice the base
so b=x
and h=2x-2

Plug in what you know (I'll do it one by one)
A=1%2F2bh
90=1%2F2bh
90=1%2F2(x)h
90=1%2F2(x)(2x-2)
90=(1%2F2)%282x%5E2-2x%29
90=%28x%5E2-x%29

%28x%5E2-x-90%29=0
(x-10)(x+9)=0
x-10=0
x=10

x+9=0
x=-9


if x=10, H=2x-2, 2(10)-2=20-2=18,
h=18, b=10

if x=-9, h=2(-9)-2=-18-2=-20
h=-20, b=-9
but since we know that the height & base cannot have a negative value, "if x=-9" wouldn't work.

the answer is h=18 and b=10