Question

A farmer has a field in the form of a parallelogram pqrs one of his horse is suffering from some leaves to take good care of the horse he tied the horse at one corner of the feet if one of the corner angles of the field is 72 degrees PQ is equals to 2 X + 5 QR is equal to 7 x + 4 are as is equals to a x + 8 and S is equals to Y + 4 then if the diagonals of field pqrs become equal by changing its angles then length of diagonal is​

Answer 1

Answer:

The field is divided in three triangles.

Since △APQ and parallelogram PQRS are on the same base PQ and between the same parallels PQ and RS.

∴ar(APQ)=

1/2ar(PQRS)

ar(PQRS)

2ar(APQ)=ar(PQRS)

But,

ar(PQRS)=ar(APQ)+ar(PSA)+ar(ARQ)(From fig.)

2ar(APQ)=ar(APQ)+ar(PSA)+ar(ARQ)

ar(APQ)=ar(PSA)+ar(ARQ)

Thus, area of △APQ=area of △PSA+area of △ARQ

To sow wheat and pulses in equal portions of the field separately, farmer should sow wheat in △APQ and pulses in other two triangles or pulses in △APQ and wheat in other two triangles.