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,

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

length

^{2}Â + breadth^{2}Â = diagonal^{2}Â [By Pythagoras Theorem]x

^{2}Â + (34 â€“ x)^{2}Â = 26^{2}x

^{2}Â + 1156 + x^{2}Â â€“ 68x = 6762x

^{2}Â â€“ 68x + 1156 â€“ 676 = 02x

^{2}Â â€“ 68x + 480 = 0x

^{2}Â â€“ 34x + 240 = 0 [Dividing by 2]By factorization method, we have

x

^{2}Â â€“ 24x â€“ 10x + 240 = 0x(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 m

^{2}.