Answer:
length = 12
width = 9
Step-by-step explanation:
We can use a system of linear equations to solve this problem. Lets make the variable L represent length and W represent width.
So we know that the length is 3 more than the width. An equation for this would be:
W = L - 3
We also know that the perimeter is 42 inches. The perimeter of a rectangle, using the variables L and W, is 2L + 2W, or 2(L + W). Using this, we can make the equation:
2(L + W) = 42
We can simplify the last equation by dividing both sides by 2:
L + W = 21
So now we have the two equations:
W = L - 3
L + W = 21
From here, there are multiple ways this question can be solved. I am going to use the substitution method here.
Knowing that W = L - 3, we can replace W in the second equation with L - 3.
L + L - 3 = 21
Add 3 to both sides.
2L = 24
Divide both sides by 2.
L = 12
Now we know that L = 12. Using this, we can replace L with 12 in the first equation to solve for W.
W = 12 - 3
W = 9
So:
L = length = 12
W = width = 9
I hope you find my answer helpful.
