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Question
A rectangular room has an area of 60 m2 and perimeter of 34 m. The length of the diagonal of the rectangular room is same as the side of a square. The area of the square (in m2) is:
Options
300
244
144
169
MCQ
Solution
169
Explanation:
Let the length be `l`
And the breadth be b
Now, `l xx b` = 60 ......(i)
`2(l + b)` = 34 ......(ii)
From (i)
`l xx b` = 60 ⇒ `l = 60/b` ......(iii)
Putting (iii) in (ii)
`2(60/b + b)` = 34
⇒ `2((60 + b^2)/b)` = 34
⇒ 60 + b2 = 17b
⇒ b2 – 17b + 60 = 0
⇒ b2 – 12b – 5b + 60 = 0
⇒ b(b – 12) – 5(b – 12) = 0
⇒ b = 12, 5
As breadth is smaller then
b = 5 m
∴ `l = 60/5` = 12 cm
∴ Diagonal = `sqrt(l^2 + b^2)`
= `sqrt((12)^2 + (5)^2`
= `sqrt(144 + 25)`
= `sqrt(169)`
= 13 m
∴ Area of square = (side)2 = (13)2 = 169 m2
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Mensuration - Area and Volume (Entrance Exam)
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