## AABC-ADEF and their perimeters are 32 cm and 24 cm respectively.If AB = 10 cm then DE = 8 cm 7.5 cm O 15 cm 57

Question

AABC-ADEF and their perimeters are
32 cm and 24 cm respectively.If AB =
10 cm then DE =
8 cm
7.5 cm
O 15 cm
573 cm​

in progress 0
2 months 2021-08-14T20:33:53+00:00 1 Answer 0 views 0

## Answers ( )

1. DE = 7.5 cm

Correct Question:

∆ABC ~ ∆DEF and their perimeters are

32 cm and 24 cm respectively.If AB =

10 cm then DE =

a.) 8 cm

b.) 7.5 cm

c.) 15 cm

d.) 573 cm

Given:

• ∆ABC is similar to ∆DEF.
• Perimeter of ∆ABC is 32 cm.
• Perimeter of ∆DEF is 24 cm.
• Meaure of AB is 10 cm

To Find:

• What is the meaure of DE ?

Solution: Since these two triangles are similar to each other. Therefore ratio of their corresponding sides will be equal. Let DE be x cm.

So,

➢ AB/DE = AC/DF = BC/EF

We have given AB and to have to find DE.

Perimeter of ABC/Perimeter of DEF = AB/DE

32/24 = AB/DE

32/24 = 10/x

x(32) = 24(10)

32x = 240

x = 240/32

x = 7.5

Hence, meaure of side DE is x = 7.5 cm.

Option C is correct.