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BITSAT 2016
Exam
BITSAT
Year
2016
Subject
Mathematics
Chapter
Area Under Curves

BITSAT 2016 · Mathematics · Area Under Curves

A wire 34 cm long is to be bent in the form of a quadrilateral of...

A wire 34cm34 \mathrm{ cm} long is to be bent in the form of a quadrilateral of which each angle is 90∘.90^{{}^{\circ}}. What is the maximum area which can be enclosed inside the quadrilateral?

Options

  1. A68cm268 \mathrm{ cm}^{2}
  2. B70cm270 \mathrm{ cm}^{2}
  3. C71.25cm271.25 \mathrm{ cm}^{2}
  4. D72.25cm272.25 \mathrm{ cm}^{2}

Correct answer

D. 72.25cm272.25 \mathrm{ cm}^{2}

Step-by-step solution

Let one side of quadrilateral be x\mathrm{x} and another side be yy so, 2(x+y)=342(x+y)=34 or (x+y)=17(x+y)=17 We know from the basic principle that for a given perimeter square has the maximum area, so,x=y\mathrm{so}, \mathrm{x}=\mathrm{y} and putting this value in equation (i) x=y=172\mathrm{x}=\mathrm{y}=\frac{17}{2} Area =x⋅y=172×172=2894=72.25=x \cdot y=\frac{17}{2} \times \frac{17}{2}=\frac{289}{4}=72.25
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