Question

In the triangle ABC, BD bisects angle B and is perpendicular to AC. If the lengths of the sides of the triangle are expressed in terms of x and y as shown, find the values of x and y.


Plz Answer It i will mark him as brainliest who explained the whole​

Answer 1

• Corresponding sides of congruent angles are congruent ...1

∠ABD = ∠CBD ... angle bisector..2

•°• AD = DC ... from 1,2

x + 1 = y + 2

x - y + 1 - 2 = 0

x - y = 1 ...a

And

∠BDA = ∠BDC = 90° ..3

•°• AB = BC ... from 1 and 3

3x + 1 = 5y - 2

3x - 5y = -2 - 1

3x - 5y = -3 ...b

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now eq:-

x - y = 1 ..a

3x - 5y = -3 ..b

multiplying eq (a) by 3

•°• 3(x - y = 1)

3x - 3y = 3 ...c

• subtracting equation B from c

3x - 5y = -3

- (3x - 3y = 3)

-2y = 0

y = 0/2

y = 0

• substituting y = 0 in eq a

•°• x - 0 = 1

x = 1

The value for x and y is 1 and 0.