Question

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

Round
your answer to the nearest tenth if necessary. Figures are not drawn to scale.

Answer 1

The measure of the side
`QR` is 8.8.

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 = (OL)/(SP) = (ON)/(RS) = (MN)/(QR) = (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 = (OL)/(SP)` (1b)

`k = (55)/(13)`

`k = (MN)/(QR)`

`QR = (MN)/(k)` (1c)

`QR = (37)/((55)/(13) )`

`QR = 8.745`

The measure of the side
`QR` is 8.8.