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

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.

Answers (1)

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
0

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