find the length and width of rectangle ABCD...a - c = 4x and c-d = x... the perimeter = 140cm
Length of a rectangle is 23cm less than 3 times its width. The perimeter of the rectangle is 82 cm. What is the length and width of the rectangle?
The length of a rectangle is 5 inches more than three times the width. The perimeter is 98 inches. Find the length and width
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To find the length and width of rectangle ABCD given the information provided, we can use the formula for the perimeter of a rectangle.
The perimeter of a rectangle is given by the formula:
Perimeter = 2 × (Length + Width)
Let's assign variables to the length and width of the rectangle. Let L be the length and W be the width.
According to the given information:
a - c = 4x -- Equation (1)
c - d = x -- Equation (2)
Perimeter = 140 cm
We need to express the length and width in terms of x to solve for their values.
Since the perimeter is the sum of all sides, we can express the formulas for the length and width:
Length = a + c
Width = b + d
Substituting a - c = 4x into the expression for Length:
Length = a + c = (4x + c) + c = 5x + 2c -- Equation (3)
Similarly, substituting c - d = x into the expression for Width:
Width = c + d = c + (c - x) = 2c - x -- Equation (4)
We can now substitute the values of Length and Width into the perimeter formula and solve for L and W:
Perimeter = 2 × (Length + Width)
140 = 2 × (5x + 2c + 2c - x)
Now, simplify the equation:
140 = 2 × (4x + 4c)
70 = 4x + 4c
Now, divide both sides of the equation by 2:
35 = 2x + 2c
Further simplifying the equation:
35 = 2(x + c)
Now, divide both sides of the equation by 2:
17.5 = x + c
We have derived an equation relating x, c, and the perimeter. However, without additional information, we cannot solve for the individual values of x and c, or determine the specific length and width of the rectangle.