The perimeter of a rectangle is 66m. if the width were doubled and the length were increased by 24m, the perimeter would be 132m. What are the length and width of the rectangle

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Let's assume the width of the rectangle is "w" meters and the length is "l" meters.

According to the problem, the perimeter of the rectangle is 66m. Using the formula for the perimeter of a rectangle, which is 2(w + l), we can write the equation as:

2(w + l) = 66

Now, if the width were doubled and the length were increased by 24m, the new perimeter would be 132m. Using the same formula for the perimeter, we can write the equation as:

2(2w + l + 24) = 132

Now, we have a system of equations. Let's solve for the values of w and l.

Equation 1: 2(w + l) = 66
Equation 2: 2(2w + l + 24) = 132

From Equation 1, let's isolate one of the variables. We'll choose w:

w + l = 66/2
w + l = 33

Now, we can substitute this expression into Equation 2:

2(2w + (33 - w) + 24) = 132
2(2w + 33 + 24 - w) = 132
2(3w + 57) = 132
6w + 114 = 132
6w = 132 - 114
6w = 18
w = 18 / 6
w = 3

Now, substitute this value back into Equation 1 to solve for l:

3 + l = 33
l = 33 - 3
l = 30

Therefore, the length of the rectangle is 30 meters and the width is 3 meters.

To find the length and width of the rectangle, let's break down the information given:

1. The perimeter of the rectangle is 66m.
2. If the width were doubled and the length were increased by 24m, the perimeter would be 132m.

Let's assign variables to the length and width of the rectangle. We can use 'L' for length and 'W' for width.

From the first statement, we know that the formula for the perimeter of a rectangle is:

Perimeter = 2 * (Length + Width)

Plugging in the values given in the first statement, we get:

66m = 2 * (L + W) ---> equation 1

Now, let's work with the second statement. It states that if the width were doubled and the length were increased by 24m, the new perimeter would be 132m. So, we can create a new equation based on this information:

132m = 2 * (L + 24 + 2W) ---> equation 2

Simplifying equation 2, we get:

132m = 2 * (L + 2W + 24)
66m = L + 2W + 24

Subtracting 24 from both sides gives us:

42m = L + 2W ---> equation 3

Now, we have a system of two equations (equations 1 and 3) with two variables (L and W). We can solve this system using either substitution or elimination method.

Let's use the substitution method:

From equation 3, we have:

L = 42m - 2W

Now substitute this value of L into equation 1:

66m = 2 * (42m - 2W + W)

Simplifying further:

66m = 84m - 4W + 2W
66m = 84m - 2W

Rearranging the equation to isolate the variable:

2W = 84m - 66m
2W = 18m
W = 9m

Now substitute the value of W back into equation 3:

L = 42m - 2 * 9m
L = 42m - 18m
L = 24m

Therefore, the length of the rectangle is 24m and the width is 9m.

original:

length --- x
width ---- y
2x + 2y = 66
x+y = 33
y = 33-x

new rectangle:
length ---- x+24
width = 2y
perimeter= 2(x+24) + 2(2y) = 132
2x + 48 + 4y = 132
2x + 48 + 4(33-x) = 132
-2x + 180 = 132

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