Question

Quadrilateral ABCD is similar to Quadrilateral WXYZ. If AB =15 WX =25 XY =15 and YZ =20, what is the measure of BC?

Answer 1

Given:

Quadrilateral ABCD is similar to Quadrilateral WXYZ.

`AB =15,\ WX =25,\ XY =15` and
`YZ =20`.

To find:

The measure of BC.

Solution:

We know that the corresponding sides of similar figures are proportional.

It is given that Quadrilateral ABCD is similar to Quadrilateral WXYZ. It means their corresponding sides are proportional.

`(AB)/(WX)=(BC)/(XY)=(CD)/(YZ)=(AD)/(WZ)`

Now,

`(AB)/(WX)=(BC)/(XY)`

After substituting the given values, we get

`(15)/(25)=(BC)/(15)`

`(3)/(5)=(BC)/(15)`

Multiply both sides by 15.

`(3)/(5)* 15=(BC)/(15)* 15`

`9=BC`

Therefore, the measure of BC is 9 units.