17. In AABC, BD bisects ZB and perpendicular to AC. If the length of the sides of the triangle are expressed in terms of x and y (as shown in the figure), then the values of x and y respectively
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In △ABD and △CBD
BD=BD (common)
∠ADB=∠CDB (each 90∘)
∠ABD=∠CDB ( BD bisect ∠B)
△ABD≅△CDB (by ASA)
⇒3x+1=5y−2 (CPCT)
⇒x= 35y−3 .....(1)
⇒x+1=y+2 (CPCT)
⇒x=y+1 .........(2)
From (1) and (2)
⇒5y−3=3(y+1)
⇒5y−3y=3+3
⇒2y=6
⇒y=3
put y=3 in (2)
x=3+1
∴x=4