Question

1. If the height h of a triangle is 3 inches less than the length of the base b, and the area A of the triangle is 19 times the length of the base, find b and h.

Answer 1

h = Height
b = Base
A = Area
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we know that the Height is 3" less than Base
h = b -3

we also know that the Area of the triangle is 19 times Base
\(Area = \cfrac{1}{2}\times base \times height \implies 19base\implies 19b\)

so we can say that
\(\bf 19b = \cfrac{1}{2}bh\\
\textit{but we know that } h = b-3\\
19b = \cfrac{1}{2}bh\implies 19b = \cfrac{1}{2}b(b-3) \implies 19b = \cfrac{b(b-3)}{2}\\
\textit{let's multiply both sides by 2}\\
19b = \cfrac{b(b-3)}{2} \implies 38b = b^2-3b\)

solve for "b" to find the Base
keep in mind that Height is just Base -3