Question

Question 5

Two similar triangles are shown in the diagram below, where
AABC - ADEF.
Based on the dimensions in the diagram, what is the
perimeter of AABC?
A-9 in.
B-10 in.
C-9.5 in.
D-10.5 in.

Answer 1

Perimeter of ΔABC is 9.5 in.

Explanation:

Given:

ΔABC
`\sim` ΔDEF

DE = 6 in.

EF = 5.25 in.

DF = 3 in.

AB = 4 in.

We need to find the Perimeter of ΔABC.

Solution:

First we will find the sides of ΔABC.

Now By Triangle similarity property which states that:

"When two triangles are similar the the ratio of their corresponding sides are equal."

From Above property we can say that;

`(AB)/(DE) =(BC)/(EF)=(AC)/(DF)\\\\(4)/(6)=(BC)/(5.25)=(AC)/(3)`

Now we will find BC and AC

`(4)/(6)=(BC)/(5.25)\\\\BC = (4*5.25)/(6)= 3.5 \ in`

Also;

`(4)/(6)=(AC)/(3)\\\\AC = (4*3)/(6) = 2 \ in`

Now In ΔABC

AB = 4 in

BC = 3.5 in

AC =2 in.

Now Perimeter of ΔABC can be calculated as sum of all sides.

Perimeter of ΔABC = AB +BC +AC = 4 + 3.5 + 2 = 9.5 in

Hence Perimeter of ΔABC is 9.5 in.