Question
The area of a rectangle is 56 cm. The length is 2 cm more than x and the width is 5 cm less than
twice x. Solve for x. Round to the nearest whole number.
twice x. Solve for x. Round to the nearest whole number.
Answers
GPT 3.5
Let x represent the width of the rectangle.
Length = x + 2
Width = 2x - 5
Area of rectangle = Length x Width
56 = (x + 2)(2x - 5)
56 = 2x^2 - 5x + 4x - 10
56 = 2x^2 - x - 10
2x^2 - x - 66 = 0
Using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a
x = (1 ± √(1 + 4(2)(66))) / 4
x = (1 ± √(1 + 528)) / 4
x = (1 ± √529) / 4
x = (1 ± 23) / 4
Therefore, x = (1 + 23) / 4 or x = (1 - 23) / 4
x = 24 / 4 or x = -22 / 4
x = 6 or x = -5.5
Since a negative value does not make sense for the width, x = 6 cm.
Therefore, the width of the rectangle is 6 cm, the length is 8 cm, and the area is 56 cm^2.
Length = x + 2
Width = 2x - 5
Area of rectangle = Length x Width
56 = (x + 2)(2x - 5)
56 = 2x^2 - 5x + 4x - 10
56 = 2x^2 - x - 10
2x^2 - x - 66 = 0
Using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a
x = (1 ± √(1 + 4(2)(66))) / 4
x = (1 ± √(1 + 528)) / 4
x = (1 ± √529) / 4
x = (1 ± 23) / 4
Therefore, x = (1 + 23) / 4 or x = (1 - 23) / 4
x = 24 / 4 or x = -22 / 4
x = 6 or x = -5.5
Since a negative value does not make sense for the width, x = 6 cm.
Therefore, the width of the rectangle is 6 cm, the length is 8 cm, and the area is 56 cm^2.