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# A farmer has a square plot of land, where he wants to grow five different crops at a time. One-half of the area in the middle, he wants to grow wheat but in rest of the four equal triangular parts, he wants to grow different crops. p and q are the mid-points of sides CA and CB respectively of a triangular part ABC right-angled at c . Prove that .

## The correct answer is: Hence proved

### Solution :-

Aim :- Prove that

Hint :- Applying pythagoras theorem to both triangles AQC and PBC. find the AQ^{2} and BP^{2} add them and substitute proper conditions to prove the condition .

Explanation(proof ) :-

Given, p is midpoint of CA i.e PC = ½ AC

Q is mid point of BC i.e QC = ½ BC

Applying pythagoras theorem to triangle AQC we get ,

As we know QC = ½ BC we get — Eq1

Applying pythagoras theorem to triangle PBC we get ,

As we know PC = ½ AC we get — Eq2

Applying pythagoras theorem to triangle ABC we get ,

— Eq3

Adding Eq1 and Eq2 we get ,

Substitute Eq 3 in the above , we get

Hence proved

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