Question

Trapezoid MNPQ is similar to Trapezoid RSTU. What is the length of the "x" on the misside side NP ? Also, what is the length of "y" on the missing side TU?

Answer 1

`x = 15`

`y = 25`

Explanation:

Given

See attachment for MNPQ and RSTU

Required

Find x and y

To solve this question, we make use of equivalent ratios of corresponding side lengths.

The ratio of corresponding sides are:

`MN : RS`

`NP : ST`

`PQ : TU`

`MQ : RU`

From the attachment, we have:

`MN : RS \to 18 : 30`

`NP : ST \to x : 25`

`PQ : TU \to 15 : y`

To solve for x, we equate
`MN : RS` and
`NP : ST`

`18 : 30 = x : 25`

Express as fraction

`(18 )/( 30 )= (x )/( 25)`

Make x the subject

`x = 25 * (18 )/( 30 )`

`x = (25 * 18 )/( 30 )`

`x = (450)/( 30 )`

`x = 15`

To solve for y, we equate
`MN : RS` and
`PQ : TU`

`18 : 30 = 15 : y`

Express as fraction

`(18 )/( 30 )= (15 )/( y)`

Make y the subject

`y = 15 * (30 )/( 18 )`

`y = (15 *30)/( 18 )`

`y = (450)/( 18 )`

`y = 25`