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

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