Question

In this question, all lengths are in centimetres. Given AB:AC = 1:2 show that AC:BC = 2:3

Answer 1

The complete data is,

Line AB: 3x-4

Line BC: 7x-2

Line AC: 2x+12

Given:

Line AB: 3x-4

Line BC: 7x-2

Line AC: 2x+12

AB:AC = 1:2

To find:

Show that AC:BC = 2:3

Solution:

From given, we have,

AB : AC = 1 : 2

⇒ AB/AC = 1/2

⇒ (3x - 4)/(2x + 12) = 1/2

⇒ 2x + 12 = 2(3x - 4)

⇒ 2x + 12 = 6x - 8

⇒ -4x = -20

∴ x = 5

Now consider,

AC : BC

⇒ AC/BC

= (2x + 12)/(7x - 2)

= [2(5) + 12] / [7(5) - 2]

= 22/33

= 2/3

⇒ AC/BC = 2/3

∴ AC : BC = 2 : 3

Hence proved.