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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: -

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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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