Question

In $△$PRS in Figure 2, $\overline{RT}$ is the altitude to side $\overline{PS}$, and $\overline{QS}$ is the altitude to side $\overline{PR}$. If RT = 7, PR = 8, and QS = 9, calculate the length of side $\overline{PS}$.

• A. $5.14$
• B. $6.22$
• C. $7.87$
• D. $10.29$
• E. $13.44$

Answer 1

The correct option is D $10.29$

Area of a triangle $=\frac{1}{2}\times$ base $\times$ height (or altitude)

Here, when the base is $PS$, the corresponding altitude is $RT$ while when the base is $PR$, the altitude is $QS$

Equating the areas, we have $\frac{1}{2}\times PS\times RT=\frac{1}{2}\times PR\times QS$

$\Rightarrow PS\times 7=8\times 9$

$\Rightarrow PS=\frac{72}{7}=10.29$