Question

Find the value of a that makes AABC~ ADEF.

B.
6
When a =
21
4x-2
D
2x + 4
12
the triangles are similar.

Answer 1

X= 5

Explanation:

If 2 triangles are similar then their corresponding side ratio are proportional

∆ABC ~∆DEF

Then

AB/DE = BC/EF = AC/DF

AB/DE = BC/EF = AC/DF6/4 = 21/2x+4 = 4x-2/12 when we simplify them

3/2 = 21/2x+4 = 2x-1/6

3/2 = 21/2x+4 = 2x-1/63/2 = 21/2x+4 .............. criss cross

3(2x+4) = 42

3(2x+4) = 422x+4 = 14

3(2x+4) = 422x+4 = 142x=14 - 4 = 10

3(2x+4) = 422x+4 = 142x=14 - 4 = 102x/2 = 10/2

3(2x+4) = 422x+4 = 142x=14 - 4 = 102x/2 = 10/2x = 5 ........we solve the value of x

In order to take x = 5 we must check it by inserting to the other proportion

6/4 = 4x-2/12 ........ when we simplify it

3/2 = 2x-1/6 ........ then we will insert 5 in place of x

3/2 = 9/6....... when we simplify it by 3

3/2 = 3/2 ..... so the are proportional ( equal )

so the value of x is 5