The length of a square with a circumference of 32 meters is one more than two times the width. What is the width of the square?
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Correct Question: The length of a rectangle with a circumference of 32 meters is one more than two times the width. What is the width of the rectangle? Because, in a square, all the four sides are equal while according to the given condition they are not hence it must be a rectangle then as in rectangle, the lengh and width aren't the same. Answer: Length = 11 m Width = 5 m Solution: Let the width and height of the rectangle be x and y respectively. According to the question, ⇒ Perimeter = 32 m ⇒ Sum of all sides = 32 m ⇒ x + y + x + y = 32 ⇒ 2(x + y) = 32 ⇒ x + y = 16 m ...(i) Also, The length of the rectangle is one more than twice the width which means, ⇒ Length = 2×Width + 1 ⇒ x = 2y + 1 ...(ii) Substituting the value of x from eq.(ii) in eq.(i), we get ⇒ (2y + 1) + y = 16 ⇒ 2y + 1 + y = 16 ⇒ 2y + y = 16 - 1 ⇒ 3y = 15 ⇒ y = 5 m Now, Put y = 5 in eq.(i), ⇒ x + y = 16 ⇒ x + 5 = 16 ⇒ x = 11 m Hence, The length and the width of the given rectangle are 11 m and 5 m respectively.
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Correct Question: The length of a rectangle with a circumference of 32 meters is one more than two times the width. What is the width of the rectangle? Because, in a square, all the four sides are equal while according to the given condition they are not hence it must be a rectangle then as in rectangle, the lengh and width aren't the same. Answer: Length = 11 m Width = 5 m Solution: Let the width and height of the rectangle be x and y respectively. According to the question, ⇒ Perimeter = 32 m ⇒ Sum of all sides = 32 m ⇒ x + y + x + y = 32 ⇒ 2(x + y) = 32 ⇒ x + y = 16 m ...(i) Also, The length of the rectangle is one more than twice the width which means, ⇒ Length = 2×Width + 1 ⇒ x = 2y + 1 ...(ii) Substituting the value of x from eq.(ii) in eq.(i), we get ⇒ (2y + 1) + y = 16 ⇒ 2y + 1 + y = 16 ⇒ 2y + y = 16 - 1 ⇒ 3y = 15 ⇒ y = 5 m Now, Put y = 5 in eq.(i), ⇒ x + y = 16 ⇒ x + 5 = 16 ⇒ x = 11 m Hence, The length and the width of the given rectangle are 11 m and 5 m respectively.