Question

a farmer was having a field in the form of a parallelogram pqrs he took any point a on rs (=10cm) and joined it to points p and q such that the height of ∆apq is 8 cm

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Answer 1

Step-by-step explanation:

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)=

2

1

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.