Length of a rectangle is five more than twice its breadth. If its area is 273 sq.cm., then the area (in sq. cms) of the circle, whose radius is equal to the breadth of the rectangle, is:?

Question

Length of a rectangle is five more than twice its breadth. If its area is 273 sq.cm., then the area (in sq. cms) of the circle, whose radius is equal to the breadth of the rectangle, is:?

346.5
123.25
140
210

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 1 : 346.5

Given :

Area of rectangle = 273 cm²

The radius of circle = breadth of the rectangle

Formula used :

Area of rectangle = length × breadth

Area of circle = π r²

Solution :

Let the breadth of rectangle be x cm

∴ the length of rectangle = (2x + 5) cm

∴ x × (2x + 5) = 273

⇒ 2x² + 5x = 273

⇒ 2x² + 5x - 273 = 0

⇒ 2x² + 26x - 21x - 273 = 0

⇒ 2x(x + 13) - 21(x + 13) = 0

⇒ (x + 13)(2x - 21) = 0

If x + 13 = 0

then x = -13 (breadth can't be negative)

If 2x - 21 = 0

then x = 21/2

Breadth of rectangle = (21/2) cm

Now, Breadth of rectangle = radius of circle

∴ r = 21/2 cm

Area of circle = π r²

⇒ Area of circle = (22/7)(21/2)(21/2)

Area of circle = 346.5 cm²