Question 884649: A carpenter is making a backyard deck. In his measurements, he has determined that he needs to make a support triangle with an area 22 mē. He knows that the base must be 1 less than 3 times the height. If the base is represented by 3x - 1 and the height = x, find the dimensions of the triangle.
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! A carpenter is making a backyard deck. In his measurements, he has determined that he needs to make a support triangle with an area 22 mē. He knows that the base must be 1 less than 3 times the height. If the base is represented by 3x - 1 and the height = x, find the dimensions of the triangle.
base = 3x - 1
height = x
area of triangle = (1/2)bh
22 = (1/2)(3x-1)(x)
44 = (3x-1)(x)
44 = 3x^2-x
0 = 3x^2-x-44
0 = 3x^2-12x+11x-44
0 = (3x^2-12x)+(11x-44)
0 = 3x(x-4)+11(x-4)
0 = (x-4)(3x+11)
x = {-11/3, 4}
throw out the negative solution (extraneous) leaving
x = 4 m (height)
.
Base:
3x - 1 = 3(4) - 1 = 12 - 1 = 11 m (base)
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