Question

In ABC, AB = AC and A = 60°. AB = 3x + 5, BC = 3y + 2 and AC = 7x − 11. Find the values of x and y.

Answer 1

Given:

AB = 3x + 5, BC = 3y + 2, AC = 7x − 11

Since AB = AC, we equate the two:

3x + 5 = 7x − 11

7x − 3x = 5 + 11

4x = 16

x = `16/4`

∴ x = 4

Now substitute x = 4 in AB and AC:

AB = 3(4) + 5

AB = 12 + 5

∴ AB = 17

AC = 7(4) − 11

AC = 28 − 11

∴ AC = 17

So, AB = AC = 17

Since △ABC is isosceles with ∠A = 60°, the other two angles must be:

`angleB = angleC = (180^circ - 60^circ)/2 = 60^circ`

Thus, △ABC is equilateral, meaning:

AB = BC = AC

So, here,

BC = 17

But, BC = 3y + 2, hence:

3y + 2 = 17

3y = 17 − 2

3y = 15

y = `15/3`

∴ y = 5