# The base of a triangle is 3 ft more than the height. If the area is 14 ft², find the base and the height.

Question
The base of a triangle is 3 ft more than the height. If the area is 14 ft², find the base and the height.

2021-02-06
The area of a triangle with base b and height h is given by: $$\displaystyle{A}=\frac{{1}}{{2}}{b}{h}$$
We are given that b=h+3 so we have: $$\displaystyle{14}=\frac{{1}}{{2}}{\left({h}+{3}\right)}$$ have
Multiply both sides by 2: $$\displaystyle{28}={h}^{{2}}+{3}{h}$$
Subtract 28 from both sides: $$\displaystyle{0}={h}^{{2}}+{3}{h}-{28}$$
Factor the right side: $$\displaystyle{0}={\left({h}+{7}\right)}{\left({h}-{4}\right)}$$
By zero product property: h=-7,4
The height cannot be negative so we have: h=4ft
which follows that: b=4+3
b=7ft

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