Question

A carpet size 5 metre *2 metre has 25 cm wide red border. The inner part of the carpet is blue in colour find the area of blue portion what is the ratio of the areas of red portion to Blue portion

Answer 1

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Given dimensions of the carpet is 8m by 5m.

Length, l = 8m and breadth, b = 5m

Area of the carpet = 8 × 5 = 40 sq m

Let the width of the border be 'x'

Length of the border = 8 − 2x

Breadth of the border = 5 − 2x

Area of inner (carpet without border) rectangle = (8 − 2x) × (5 − 2x)

                                                                         = 40 − 26x + 4x2

Given area of the border = 12 sq m

Area of border = area of carpet  − area of carpet without border

12 = 40 − ( 40 − 26x + 4x2)

⇒ 12 = 40 − 40 + 26x − 4x2

⇒ 12 = 26x − 4x2

⇒ 6 = 13x − 2x2

⇒ 2x2 − 13x + 6 = 0

⇒ 2x2 − 12x  − x + 6 = 0

⇒ 2x (x − 6) −1( x − 6) = 0

⇒ (x − 6)(2x −1) = 0

⇒ (x − 6) = 0 or (2x −1) = 0

∴ x = 6 or x = 1/2

But x ≠ 6, hence x = 1/2

Width of the border is (1/2) m.

the asnwer for your question is 6.75m2;13:27