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The maximum area of a reactangle whose sides pass through the angular ponts of a given resctangle of sides a and b is : ans is 1/2(a+b)2.. plzz explain

The maximum area of a reactangle whose sides pass through the angular ponts of a given resctangle of sides a and b is :


ans is 1/2(a+b)2..


plzz explain

Grade:11

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
8 years ago
Ans:Hello student, please find answer to your question
Let the angular points of the given rectangle to be O (0, 0), A (a, 0), B (a, b) and C (0, b).
Diagonal length:
\sqrt{a^{2}+b^{2}}
Since the rectangle passing through angular points of rectangle OABC. Then side length of one side must be equal to diagonal length
Let the
c + d = \sqrt{a^{2}+b^{2}}
Let side length of other side be
e + f
We have
e = \sqrt{a^{2}-c^{2}}
f = \sqrt{b^{2}-d^{2}}
Area of rectangle
A = (c+d)(e+f)
A = \sqrt{a^{2}+b^{2}}(\sqrt{a^{2}-c^{2}}+\sqrt{b^{2}-(\sqrt{a^{2}-b^{2}}-c)^{2}})
\frac{\partial A}{\partial c} = 0
\Rightarrow c = \frac{a^{2}\sqrt{a^{2}+b^{2}}}{2}
A_{max} = \frac{(a+b)^{2}}{2}

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