Question

In this question, all lengths are in cm. ABC. 3x-4, 2x+12, 7x-2. Given that AB:AC = 1:2 Show that AC:BC = 2:3

Answer 1

Explanation:

First find x:

AB:AC=1:2

2(3x-4)=2x+12

6x-8=2x+12

4x-8=12

4x=20

x=5

Substitute:

AC=2x+12

=(2x5)+12

=10+12

=22

BC=7x-2

=(7x5)-2

=35-2

=33

22/33=2/3

Therefore AC:BC = 2:3

Answer 2

Answer: AC : BC = 22 : 33 = 2 : 3

Explanation:

Since we have given that

AB = 3x-4

AC= 2x+12

BC = 7x-2

And AB: AC = 1 : 2

and To show : AC : BC = 2 : 3

So, it becomes ,

`(AB)/(AC)=(3x-4)/(2x+12)=(1)/(2)\\\\2(3x-4)=2x+12\\\\6x-8=2x+12\\\\6x-2x=12+8\\\\4x=20\\\\x=(20)/(4)\\\\x=5`

So, AC: BC becomes:

`(AC)/(BC)=(3x-4)/(7x-2)=(2(5)+12)/(7(5)-2)=(22)/(33)=(2)/(3)`

Hence, proved.