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Possible diagonals of a rectangle with fixed perimeter

Possible diagonals of a rectangle with fixed perimeter

IP 3
7 marks

A rectangle has perimeter \(20\) cm, area \(A\) cm\(^2\) and diagonal of length \(d\) cm.

  1. Show that \(A=50-\dfrac{d^2}{2}\).[2]
  2. Explain why the length and the breadth of the rectangle are the roots of the equation \(x^2-10x+A=0\).[2]
  3. Hence find the range of possible values of \(d\).[3]

Solution:

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Answer:(a) shown (b) shown (c) \(5\sqrt{2}\le d<10\)

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