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

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

Step-by-step 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 ,

$\dfrac{AB}{AC}=\dfrac{3x-4}{2x+12}=\dfrac{1}{2}\\\\2(3x-4)=2x+12\\\\6x-8=2x+12\\\\6x-2x=12+8\\\\4x=20\\\\x=\dfrac{20}{4}\\\\x=5$

So, AC: BC becomes:

$\dfrac{AC}{BC}=\dfrac{3x-4}{7x-2}=\dfrac{2(5)+12}{7(5)-2}=\dfrac{22}{33}=\dfrac{2}{3}$

Hence, proved.