Question

Find the values of x and y?​

Answer 1

Answer:

x = 7; y = 4  

Step-by-step explanation:

∆ABC is an isosceles triangle.

∴ AC = BC and

(1) 3x - 5 = y + 12

∆ACD is an equilateral triangle.

∴ AC = AD and

(2) 3x - 5 = 5y - 4

From (1) and (2),

y + 12 = 5y - 4

y + 16 = 5y

    4y = 16

(3)   y =   4

Substitute (3) into (1)

3x - 5 = 4 + 12

3x - 5 = 16

     3x = 21

       x = 7

x = 7; y = 4

Check:

AC = 3x  -   5 = 3(7) -   5 = 21 -  5 = 16

BC =   y  + 12 = 4     + 12 = 16

AD = 5y -   4 = 5(4)  -   4 = 20 - 4 = 16

OK .