Question

Q1. Perimeter of a parallelogram is 150 cm. One of its sides is greater than the other side
by 25 cm. Find the lengths of all sides.​

Answer 1

Step-by-step explanation:

Let the length of one side be x cm

Therefore,

Length of other side is (x+25) cm

Therefore,

A/Q,

perimeter of parallelogram=l×b

=>150=x(x+25)

=>150=x²+25x

=>x²+25x-150=0

=>x²+30x-5x-150=0

=>x(x+30)-5(x+30)=0

=>(x-5)(x+30)=0

Therefore,

Either, x+30=0

=>x=-30 [which is not possible]

or,x-5=0

=>x=5

Therefore x=5cm

Hence the two sides are:-

x=5cm

x+25=30cm

Answer 2

Solution :

Let [] ABCD be a parallelogram and the length of AD be x cm

•/(AB) = (x + 25) cm .. {opposite side parallelogram}

/(AD)=/(BC)= xcm

/(AB)=/(DC)=(x+ 25) cm

perimeter of [] ABCD = 105cm

•/(AB) + /(BC) + /(DC) + /(AD) = 105

°(x+25) + x + (x+25) + x = 150

°4x = 50 = 150

°4x = 100

°/(AD)=/(BC)= x =25cm

/(AB)=/(DC) = x + 25 = 25 + 25 = 50 cm

the length of the sides of the parallelogram are 25 cm, 50cm, 25cm, 50cm.