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Question
If the perimeter of a rectangular plot is 68 m and the length of its diagonal is 26 m, find its area.
Solution
Perimeter = 68 m and diagonal = 26m
Length + breadth = = 34m
Let length = xm
then breadth = (34 – x)m
According to the condition,
l2 + b2 = h2
(x)2 + (34 - x)2 = (26)2
⇒ x2 + 1156 + x2 - 68x = 676
⇒ 2x2 - 68x + 1156 - 676 = 0
⇒ 2x2 - 68x + 480 = 0
⇒ x2 - 34x + 240 = 0 ...(Dividing by 2)
⇒ x2 - 24x - 10x + 240 = 0
⇒ x(x - 24) -10(x - 24) = 0
⇒ (x - 24)(x - 10) = 0
Either x - 24 = 0,
then x = 24
or
x - 10 = 0,
then x = 10
∵ Length is greater than breadth
∴ Length = 24m
and breadth = (34 - 24) = 10m
and Area = l x b = 24 x 10 = 240m2.
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