Question

Pentagons ABCDF and JKLMN below are similar, but not necessarily drawn to scale. Find the Values of X and Y.

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

BC = 20 mm

DF = 30 mm

AB = x

KL = 4 mm

KJ = 8 mm

MN = y

Step 02:

We must apply properties of similar figures.

`(KL)/(BC)=(MN)/(DF)`
`(4)/(20)=(y)/(30)`

4 * 30 = 20 * y

120 = 20y

120/20 = y

6 = y

`(KL)/(BC)\text{= }(KJ)/(AB)`
`(4)/(20)=(8)/(x)`

4 * x = 8 * 20

4x = 160

x = 160 / 4

x = 40

The answer is:

x = 40 mm , y = 6 mm