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.

Perimeter of ΔABC is 9.5 in.

Step-by-step explanation:

Given:

ΔABC 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;

Now we will find BC and AC

Also;

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.