Question

The area of $\Delta$ABC is $150$ square units. If $\overline{AB}=\overline{AH}=20$, then the length of $\overline{HG}$ is:

• A. $5$
• B. $12$
• C. $16$
• D. $20$

Answer 1

The correct option is B $12$

Area of $\Delta ABC=150$ sq. units

$AB=20$ units

$\frac{1}{2}\times AB\times BC=150$

$\therefore BC=15$ units

Since $\angle B$ is a right angle, $A{C}^2=A{B}^2+B{C}^2$

$\therefore A{C}^2=400+225=625$

$\therefore AC=25$ units

Since $\Delta ABC$ and $\Delta AGH$ are similar triangles,

$\frac{AH}{AC}=\frac{HG}{CB}$

$\Rightarrow \frac{20}{25}=\frac{HG}{15}$

$\therefore HG=\frac{20\times 15}{25}=12$ units