Question

Triangle PQR is similar to triangle XYZ. The length of PQ is one-half the length of XY. THe length of RP is 2 cm. Which proportion can be used to find the length of ZX?

Answer 1

`ZX = 4cm`

Explanation:

Given

`\triangle PQR` similar to
`\triangle XYZ`

`PQ = (1)/(2)XY`

`RP = 2cm`

Required

Find ZX

`\triangle PQR` similar to
`\triangle XYZ` implies that, the following sides are similar

`PQ \to XY`

`QR \to YZ`

`RP \to ZX`

To find ZX, we make use of the following equivalent ratio

`PQ : XY = RP : ZX`

Where

`PQ = (1)/(2)XY`

`RP = 2cm`

So, we have:

`(1)/(2)XY : XY = 2cm : ZX`

Express as fraction

`((1)/(2)XY )/( XY )= (2cm )/( ZX)`

`(1)/(2)= (2cm )/( ZX)`

Make ZX the subject

`ZX = 2 * 2cm`

`ZX = 4cm`