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

Let’s consider the length of the rectangular plot to be ‘x’ m

Then, breadth = (34 – x) m

Now, the diagonal of the rectangular plot is given by

length

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

^{2}+ (34 – x)^{2}= 26^{2}x

^{2}+ 1156 + x^{2}– 68x = 6762x

^{2}– 68x + 1156 – 676 = 02x

^{2}– 68x + 480 = 0x

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

x

^{2}– 24x – 10x + 240 = 0x(x – 24) – 10(x – 24) = 0

(x – 10) (x – 24) = 0

So,

x – 10 = 0 or x – 24 = 0

x = 10 or x = 24

As length is greater than breadth,

Thus, length = 24 m and breadth = (34 – 24) m = 10 m

And, area of the rectangular plot = 24 × 10 = 240 m

^{2}.