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# If the perimeter of a rectangular plot is 68 m and the length of its diagonal is 26 m, find its area.

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This question has been taken from Book:- ML aggarwal, Avichal publication, class10th, quadratic equation in one variable, chapter 5, exercise 5.5
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If the perimeter of a rectangular plot is 68 m and the length of its diagonal is 26 m, find its area.
Question no18. , ML Aggarwal, chapter 5, exercise 5.5, quadratic equation in one variable, ICSE board,

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1. Given,

Perimeter = 68 m and diagonal = 26 m

So, Length + breadth = Perimeter/2

= 68/2

= 34 m

Letâ€™s consider the length of the rectangular plot to be â€˜xâ€™ m

Then, breadth = (34 â€“ x) m

Now, the diagonal of the rectangular plot is given by

length2Â + breadth2Â = diagonal2Â [By Pythagoras Theorem]

x2Â + (34 â€“ x)2Â = 262

x2Â + 1156 + x2Â â€“ 68x = 676

2x2Â â€“ 68x + 1156 â€“ 676 = 0

2x2Â â€“ 68x + 480 = 0

x2Â â€“ 34x + 240 = 0 [Dividing by 2]

By factorization method, we have

x2Â â€“ 24x â€“ 10x + 240 = 0

x(x â€“ 24) â€“ 10(x â€“ 24) = 0

(x â€“ 10) (x â€“ 24) = 0

So,

x â€“ 10 = 0 or x â€“ 24 = 0

x = 10 or x = 24

As length is greater than breadth,

Thus, length = 24 m and breadth = (34 â€“ 24) m = 10 m

And, area of the rectangular plot = 24 Ã— 10 = 240 m2.

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