This question is from Mensuration. Mensuration is a very intuitive topic. You can expect at least one question from this topic in the **CAT exam**. The questions from Mensuration can be solved with a practical approach even if one is not completely prepared for the entire **Geometry ** section in CAT. This question hovers around a circle that is inscribed in a triangle. Then the Circle is painted. We need to find the perimeter of the rectangle. Make sure you master Mensuration by practising **CAT Previous Year Question paper**. From now on, you should not be able to look at a bucket without thinking of it as a cone carved out from another cone!

Question 22 : On a rectangular metal sheet of area 135 sq in, a circle is painted such that the circle touches opposite two sides. If the area of the sheet left unpainted is two-thirds of the painted area then the perimeter of the rectangle in inches is

- 3√π(5 + \\frac{12}{π}))
- 4√π(3 + \\frac{12}{π}))
- 5√π(3 + \\frac{12}{π}))
- 3√π(\\frac{5}{2}) + \\frac{6}{π}))

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Total area = 5 parts

So, painted area = 135 × \\frac{3}{5}) = π r^{2}

Solving r = \\frac{9}{√π})

Substituting r in l = \\frac{135}{2r})

l = \\frac{15√π}{2})

Perimeter of rectangle = 2(l + b)

= 2(\\frac{15√π}{2}) + \\frac{18}{√π}))

= 3√π (5 + \\frac{12}{π}))

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