Question

In AABC, AB = AC and AP 1 BC. If AB= (2x + 3) cm, AC = (3y-1) cm, BP = (y + 1) cm and PC = (x + 2) cm find the values of x and y.

​

Answer 1

• x = 1
• y = 2

Explanation:

Given isosceles triangle ABC with AB≅AC, altitude AP, and AB=(2x+3), AC=(3y-1), BP=(y+1), and PC=(x+2), you want the values of x and y.

Isosceles triangle

Corresponding parts of ∆ABP and ∆ACP are congruent, so we have ...

2x +3 = 3y -1

x +2 = y +1

Solution

Subtracting twice the second equation from the first gives ...

(2x +3) -2(x +2) = (3y -1) -2(y +1)

-1 = y -3 . . . . simplify

2 = y . . . . . . add 3

Substituting into the second equation, we have ...

x +2 = 2 +1

x = 1 . . . . . . . .subtract 2

The values of x and y are 1 and 2, respectively.