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?

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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