Question

if ABCD is a parallelogram with AB=2x+1, CD=3x-10 and AD=x+12, show that ABCD is a square if <ABC is 90°

Answer 1

it is given that
AB=2x+1
CD=3x-10
AD=x+12
we know that opposite sides of a Parralelogram are equal.
so,
AB=CD
=>2x+1=3x-10
=>2x-3x=-10-1
=>-x=-11
=>x=11______(i)

Substituting eq(i) we get,
AB=2(11) +1
=22+1
=23=CD
AD=x+12
=11+12
=23=BC
Hence, AB=BC=CD=AD
thus, ABCD is a square.

Answer 2

1. AB=2x+1 CD=3x-10 AD=x+12  so,  AB=CD =>2x+1=3x-10 =>2x-3x=-10-1 =>-x=-11 =>x=11______(i)   Substituting eq(i) we get,  AB=2(11) +1 =22+1 =23=CD  AD=x+12 =11+12 =23=BC  AB=BC=CD=AD  ABCD is a square.