Question

Question 282 ptsThe formula for finding the perimeter, P. of a rectangle with length l and width w is given.P= 2l + 2wWhich formula shows how the length of a rectangle can be determined from the perimeter and thewidth?

Answer 1

We have from the question, that the Perimeter of a rectangle is given by the formula:

`P=2\cdot l+2\cdot w`

That is, twice the value of the length plus twice the value of the width gives us the value of the perimeter of the rectangle.

Now, the formula which shows us the length of a rectangle determined from the perimeter and the width is that one resulting from solve for the length in the previous formula.

Then, we can follow the next steps to find it:

1. Subtract from both sides of the above formula 2w (we use here the subtraction property of equality):

`P-2w=2l+2w-2w\Rightarrow P-2w=2l_{}`

2. Divide by 2 to both sides of this equation (we use here the division property of equality):

Therefore, we have that the formula which shows us the length of a rectangle determined from the perimeter and the width is: