Question

Find the values of x and y.

Answer 1

ΔABC has two congruent angles. Therefore, it is an isosceles triangle.

Therefore we have the equation (1)  3x - 5 = y + 12.

All angles of the ΔDBC are congruent. Therefore it is an equilateral triangle.

Therefore we have the equation (2)  3x - 5 = 5y - 4

From (1) and (2) we have the equation:

5y - 4 = y + 12      add 4 to both sides

5y = y + 16     subtract y from both sides

4y = 16     divide both sides by 4

y = 4

Substitute the value of y to (1):

3x - 5 = 4 + 12

3x - 5 = 16       add 5 to both sides

3x = 21       divide both sides by 3

x = 7

Answer: x = 7 and y = 4