Description
Suppose the base and height of a triangle sum to 12, and the area of the triangle is 16 square cm. What are the dimensions (base and height) of the triangle?
Explanation & Answer
b= base
h= height
we have:
1. b + h = 12
2. b*h/2=16
substitute 1 in 2:
b(12-b)/2=16
b(12-b)=32
b^2-12b+32=0
solve for b:
b= 6+-sqrt(36-32)=6+-2
thus we have 2 solutions for b:
b1 = 8 , b2 = 4
accordingly we have 2 solutions for h
h1=4, h2 = 8
So we have 2 solutions: one with a base of 8 and height of 4 the other one is a base of 4 and height of 8.
Both solutions obey the requirements.
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