Question

KLM~PQR with a scale factor of 3:5, find the perimeter of PQR

Answer 1

We have:

KL = 6

KM = 12

LM = 15

And the given scale factor is 3:5.

The KLM and PQR triangles are similar, therefore:

KL:PQ = 3:5

KM:PR = 3:5

LM:QR = 3:5

This can also be expressed as a fraction:

$\frac{KL}{PQ}=\frac{3}{5}$

Substitue KL = 6 and find PQ:

$\begin{gathered} \frac{6}{PQ}=\frac{3}{5} \\ 6\cdot5=3\cdot PQ \\ 30=3\cdot PQ \\ \frac{30}{3}=\frac{3PQ}{3} \\ PQ=10 \end{gathered}$

For side PR:

$\frac{KM}{PR}=\frac{3}{5}$

KM = 12, so:

$\begin{gathered} \frac{12}{PR}=\frac{3}{5} \\ 12\cdot5=3\cdot PR \\ 60=3\cdot PR \\ \frac{60}{3}=\frac{3PR}{3} \\ PR=20 \end{gathered}$

And for side QR:

$\frac{LM}{QR}=\frac{3}{5}$

LM = 15, then:

$\begin{gathered} \frac{15}{QR}=\frac{3}{5} \\ 15\cdot5=3\cdot QR \\ 75=3\cdot QR \\ \frac{75}{3}=\frac{3QR}{3} \\ QR=25 \end{gathered}$

Next, the perimeter is given by:

$P=PQ+PR+QR=10+20+25=55$

Answer: The perimeter of ΔPQR is 55.