the perimeter of a rectangle is twice the sum of its length and its width. the perimeter is 40 meters and its lenth is 2 meters more then twice its width. what is the length?
p=2.(w+l) p=40 l=2+w 40=2(w+(2=w)divide by 2 20=2w=2 subtract by 2 18=2w divide by 2 l=2+w substitude w for 9 l=11 answer =11
To find the length of the rectangle, we first need to set up an equation based on the given information.
Let's denote the length of the rectangle as "L" and the width as "W".
We are given two pieces of information:
1. The perimeter of the rectangle is twice the sum of its length and its width.
2. The perimeter is 40 meters.
From the first piece of information, we can write the equation:
Perimeter = 2 * (Length + Width)
Substituting the given perimeter value of 40 meters, we can rewrite the equation as:
40 = 2 * (L + W)
We are also given that the length (L) is 2 meters more than twice its width (W). Using this information, we can write another equation:
L = 2W + 2
Now we have a system of two equations:
1. 40 = 2 * (L + W)
2. L = 2W + 2
We can solve this system of equations to find the values of L and W. Let's substitute the value of L in the first equation with the expression from the second equation:
40 = 2 * ((2W + 2) + W)
Simplifying further:
40 = 2 * (3W + 2)
40 = 6W + 4
Subtracting 4 from both sides:
36 = 6W
Dividing both sides by 6:
6 = W
Now, we can substitute the value of W back into the second equation to find L:
L = 2W + 2
L = 2(6) + 2
L = 12 + 2
L = 14
Therefore, the length of the rectangle is 14 meters.