Question

An animal enclosure is a right angled triangle with one leg being a drain

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