Question

Given the figures are similar, calculate the perimeter of the ABCDE.

Answer 1

Perimeter of the figure ABCDE will be 38 in.

Explanation:

In the figure attached two similar pentagons ABCDE and FGHIJ have been given. Since they are similar so their sides will be in the same ratio.

`(IJ)/(AE)=(HI)/(AB)`

`(4)/(12)=(2)/(AB)`

AB =
`(2* 12)/(4)=6`in

Now perimeter of pentagon ABCDE = AB + BC + CD + DE + EA

= 12 + 4 + 4 + 12 + 6

= 38 in

Therefore, perimeter of the figure ABCDE will be 38 in.

Answer 2

The perimeter of ABCDE is 38 inch.

Explanation:

From the given figure it is notices that

`AE=BC=12\text{ in}`

`ED=CD=4\text{ in}`

It is given that both figure are similar. The corresponding sides of similar figures are proportional.

Since the figures ABCDE and HIJFG are similar,therefore the corresponding sides of both figures are proportional.

In figures ABCDE and HIJFG,

`(AB)/(HI)=(AE)/(JI)`

`(AB)/(2)=(12)/(4)`

`AB=3* 2`

`AB=6`

The perimeter of ABCDE is

`AB+BC+CD+DE+AE=6+12+4+4+12=38`

Therefore the perimeter of ABCDE is 38 inch.