Question

find the perimeter of △ cbh if △ cbh ~△ feh, adeg is a parallelogram, ch = 7, fh = 10, fe = 11, and eh = 6. express your answer as a decimal if necessary.

Explanation:

Step1: Find the similarity ratio

Since $\triangle CBH\sim\triangle FEH$, the similarity ratio $k=\frac{CH}{FH}=\frac{7}{10}$.

Step2: Find the lengths of $CB$ and $BH$

We know that $\frac{CB}{FE}=\frac{CH}{FH}$ and $\frac{BH}{EH}=\frac{CH}{FH}$. Given $FE = 11$ and $EH=6$. Then $CB=\frac{7}{10}\times FE=\frac{7}{10}\times11 = 7.7$ and $BH=\frac{7}{10}\times EH=\frac{7}{10}\times6 = 4.2$.

Step3: Calculate the perimeter of $\triangle CBH$

The perimeter $P$ of $\triangle CBH$ is $P=CB + BH+CH$. Substitute $CB = 7.7$, $BH = 4.2$ and $CH = 7$ into the formula. So $P=7.7+4.2 + 7=18.9$.

Answer:

$18.9$