Question

In the ∆ABC given below, BD bisects ∠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.​

Answer 1

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In △ABD and △DBC,

BD=BD (Common)

∠ABD=∠CBD (BD bisects ∠B)

∠BDA=∠BDC (Each 90

∘

)

Thus, △ABD≅△CBD (SAS postulate)

Hence, AB = AC (By cpct)

3x+1=5y−2

3x=5y−3 (I)

Also, AD = DC (By cpct)

x+1=y+2

x=y+1 (II)

Substituting x in equation (I)

3(y+1)=5y−3

3y+3=5y−3

2y=6

∴y=3

And, x=3+1=4