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Question: A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank...

A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length x. The maximum area

enclosed by the park is –

A

px2

B

32\frac{3}{2} x2

C

12\frac{1}{2} x2

D

x3/8\sqrt{x^{3}/8}

Answer

12\frac{1}{2} x2

Explanation

Solution

Area = 12\frac{1}{2} × x × x sin q

Area = x22\frac{x^{2}}{2} sin q

® (Area)max when (sinq)max = 1

Ž max. area = x22\frac{x^{2}}{2} × 1 = x22\frac{x^{2}}{2}