Question

A farmer has a field in the shape of a right angle triangle with legs are of length 16 M and 8 M he wants to leave space in the form of a square of largest area for growing wheat and remaining area for growing vegetables find the length of the side of such a square.

Answer 1

let the field be represented by ∆ABC with <B = 90°, AB = 16 m, BC = 8 m

let the side of square be x m long.
therefore PB = BQ = PR = RQ = x m
CP = (8 - x) m, QA = (16 - x) m

ar(ABC) = ½*AB*BC
= ½ * 8 * 16
= 64 m²

ar(CPR) = ½*CP*PR
= ½ * (8-x) * x
= (4x - ½x²) m²

ar(RQA) = ½*RQ*QA
= ½ * (16-x) * x
= (8x - ½x²) m²

ar(PRQB) = PR² = x² m²

ar(ABC) = ar(CPR) + ar(RQA) + ar(PRQB)
64 = 4x - ½x² + 8x - ½x² + x²
64 = 12x
x = 16/3 m

therefore the side of the square is 16/3 m

Answer 2

Explanation:

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