By solving a system of equations we will find the dimensions of the rectangle, and with these, we will see that the area is equal to 82.31 m^2
For a rectangle of length L and width W, the perimeter is:
P = 2*L + 2*W
In this case, we know that the perimeter is equal to 38m, then:
38m = 2*L + 2*W
We also know that if we subtract 3 meters from the length and 2 meters from the breadth, the length will e 2 times the breadth.
This is written as:
(L - 3m) = 2*(W - 2m)
Then we have a system of equations:
38m = 2*L + 2*W
(L - 3m) = 2*(W - 2m)
To solve this, we isolate one of the variables in one of the equations, I will isolate L on the second equation:
L = 2*(W - 2m) + 3m
Replacing that on the other equation we get:
38m = 2*(2*(W - 2m) + 3m) + 2*W
Now we can solve this for W.
38m = 4*(W - 2m) + 6m + 2*W
38m = 4*W - 2m + 2*W
38m + 2m = 6*W
40m = 6*W
40m/6 = W = 6.67m
Then the length is:
L = 2*( 6.67m - 2m) + 3m = 12.34 m
So the area of the rectangle is:
A = L*W = 12.34m*6.67m = 82.31 m^2
If you want to learn more about systems of equations, you can read:
https://brainly.com/question/13729904
