the perimeter of a rectangle is 70m. if the width were doubled and length were increased by 24m, the perimeter would be 142m. what are the length and width of the rectangle?

W+W+L+L=70

(2W)+(2W)+(L+24)+(L+24)=142

Solve for W in terms of L.
W+W+L+L=70
W=(70-2L)/2
Use substitution to find L.
(2[(70-2L)/2])+(2[(70-2L)/2])+(L+24)+(L+24)=142
Then Plug the L value back into W=(70-2L)/2 to find W

To solve this problem, we need to set up a system of equations based on the given information.

Let's represent the length of the rectangle as "L" and the width of the rectangle as "W".

From the first statement, we know that the perimeter of the rectangle is 70m. The formula for the perimeter of a rectangle is P = 2L + 2W. So we can write the equation as:
2L + 2W = 70 (equation 1)

From the second statement, if the width were doubled and the length were increased by 24m, the new perimeter would be 142m. So we can write the second equation as:
2(L + 24) + 2(2W) = 142 (equation 2)

Now, we can solve these two equations simultaneously to find the values of L and W.

First, let's simplify equation 2:
2L + 48 + 4W = 142
2L + 4W = 94 (equation 3)

Next, let's solve equation 1 and equation 3 simultaneously. We can use the method of substitution or elimination to do this.

Using the elimination method, let's multiply equation 1 by 2:
4L + 4W = 140 (equation 4)

Now, we can subtract equation 3 from equation 4 to eliminate the variable W:
(4L + 4W) - (2L + 4W) = 140 - 94
2L = 46

Divide both sides of the equation by 2 to solve for L:
L = 23

Now, substitute the value of L into equation 1 to find the value of W:
2(23) + 2W = 70
46 + 2W = 70
2W = 70 - 46
2W = 24

Divide both sides of the equation by 2 to solve for W:
W = 12

Therefore, the length of the rectangle is 23m and the width of the rectangle is 12m.