The area of a triangle whose height is 1 more than 6 times its base is 13 square feet. If the base of the triangle is x feet, which equation models this situation?
Question
Answer:
We must know that the are of the triangle is given by definition byA = (1/2) * (b) * (h)
where
b = base
h = height
Substituting the values
A = (1/2) * (x) * (1 + 6x)
A = (1/2) * (x + 6x ^ 2)
Since the area is 13 then
(1/2) * (x + 6x ^ 2) = 13
Clearing x we have
6x ^ 2 + x = 26
6x ^ 2 + x-26 = 0
(x-2) * (x + 13/6) = 0
As we look for the base of a triangle then x> 0
x = 2
answer
the base is x = 2
6x ^ 2 + x = 26
solved
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