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
length2 + breadth2 = diagonal2 [By Pythagoras Theorem]
x2 + (34 – x)2 = 262
x2 + 1156 + x2 – 68x = 676
2x2 – 68x + 1156 – 676 = 0
2x2 – 68x + 480 = 0
x2 – 34x + 240 = 0 [Dividing by 2]
By factorization method, we have
x2 – 24x – 10x + 240 = 0
x(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 m2.