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Question:) A carpet is laid on the floor of a room 8 m by 5 m. If the area of the border is 12 m square, find its width.
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Question:) A carpet is laid on the floor of a room 8 m by 5 m. If the ...
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.
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Question:) A carpet is laid on the floor of a room 8 m by 5 m. If the area of the border is 12 m square, find its width.
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Question:) A carpet is laid on the floor of a room 8 m by 5 m. If the area of the border is 12 m square, find its width. for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Question:) A carpet is laid on the floor of a room 8 m by 5 m. If the area of the border is 12 m square, find its width. covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Question:) A carpet is laid on the floor of a room 8 m by 5 m. If the area of the border is 12 m square, find its width..
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