Question

Quadrilateral LMNO is similar to quadrilateral PQRS. Find the measure of side QR.

Answer 1

Answer:

The measure of the side $QR$ is 8.8.

Step-by-step explanation:

Since $LMNO \sim PQRS$, then $SP \propto OL$, $RS \propto ON$, $RQ \propto MN$ and $QP \propto LM$. From figure we have the following relationship:

$k = \frac{OL}{SP} = \frac{ON}{RS} = \frac{MN}{QR} = \frac{ML}{QP}$ (1)

Where $k$ is the proportionality ratio.

If we know that $SP = 13, OL = 55, MN = 37$, then the measure of side $QR$ is:

$k = \frac{OL}{SP}$ (1b)

$k = \frac{55}{13}$

$k = \frac{MN}{QR}$

$QR = \frac{MN}{k}$ (1c)

$QR = \frac{37}{\frac{55}{13} }$

$QR = 8.745$

The measure of the side $QR$ is 8.8.