Question

ABC is an equilateral triangle. If AB = 2x − 1, BC = y + 7, AC = 2y + 3, find x and y.

Answer 1

Here, ABC is an equilateral triangle, and the sides are given as:

AB = 2x − 1,

BC = y + 7,

AC = 2y + 3

Also, in an equilateral triangle, all three sides are equal:

AB = BC = AC

Now, we can set it up as equations:

(1) AB = BC

2x − 1 = y + 7     ...(i)

(2) BC = AC

y + 7 = 2y + 3     ...(ii)

Let’s solve equation (ii):

y + 7 = 2y + 3

7 − 3 = 2y − y

∴ y = 4

Substitute y = 4 in equation (i):

2x − 1 = 4 + 7

2x − 1 = 11

2x = 12

x = `12/2`

∴ x = 6

Hence, x = 6 and y = 4.