Question

Triangle ABC is similar to Triangle DEF. Use the similar triangles to

answer the questions. (The triangles are not to scale.)
(In pic)
a.) Find the length of the BC and DF.
b.) Find the perimeter of each triangle

please help ! thanks :)

Answer 1

Below in bold.

Explanation:

As they are similar corresponding sides are in the same proportion so

3/2 = BC/3

2BC = 3*3

2BC = 9

BC = 4.5.

3/2 = 5/DF

3DF = 2*5

DF = 2*5 / 3

= 3.33...

Perimeter of ABC = 3 + 4.5 + 5 = 12.5.

Perimeter of DEF = 2 + 3 + 3.33.. = 8.33...

Answer 2

BC = 4.5 cm

DF = 10/3 cm

Explanation:

Corresponding sides of similar triangles are in same ratio

`(BC)/(EF)=(AB)/(DE)\\\\(BC)/(3) =(3)/(2)\\\\BC = (3)/(2)*3\\\\BC = (9)/(2)\\\\BC = 4.5 cm`

`(DF)/(AC)=(DE)/(AB)\\\\(DF)/(5)=(2)/(3)\\\\DF = (2)/(3)*5\\\\DF = (10)/(3)`

Perimeter of ΔABC = 3 + 5 +4.5 = 12.5cm

Perimeter of ΔDEF = 2 + 3 + 3.3 = 8.3 cm