Question

In $△YVW$, $\overline{VX}$ is the altitude to side $\overline{YW}$, and $\overline{ZW}$ is the altitude to side $\overline{YV}$. If $\overline{VX}=3$, $\overline{YV}=4$, and $\overline{ZW}=5$, find the length of side $\overline{YW}$.

• A. $4.157$
• B. $5.303$
• C. $6.667$
• D. $6.928$
• E. $8.660$

Answer 1

Answer: (C)

$6.667$

Area of a triangle is given by $\frac{1}{2}\times$ base $\times$ height

Area of $\Delta VYW=\frac{1}{2}\times WZ\times VY$

Area of $\Delta VYW$ is also given by $\frac{1}{2}\times VX\times WY$

Equating the two expressions of areas, we have

$\frac{1}{2}\times WZ\times VY=\frac{1}{2}\times VX\times WY$

$\Rightarrow WZ\times VY=VX\times WY$

$\therefore WY=\frac{5\times 4}{3}=6.667$