Question

A student was asked to use the formula for the perimeter of a rectangle, P = 2ℓ + 2w, to solve for ℓ. The student came up with an answer, P − 2w = 2ℓ. What error did the student make? Complete the explanation. Then solve for ℓ.

Answer 1

• you have correctly described the error
• ℓ = (P/2) -w

Explanation:

To complete the solution, the equation the student came up with must be divided by 2:

P/2 -w = ℓ

Then the sides can be swapped to give ...

ℓ = (P/2) - w

Answer 2

The value of l will be:

`l=(P)/(2)-w`

Explanation:

We know that the formula of a perimeter(P) of a rectangle in terms of the length(l) and width(w) is given by:

`P=2l+2w`

Now, the students came up by solving the equation for l as:

`2l=P-2w`

i.e. the students only rearranged the terms in such a way i.e. the variable term is on one side of the equation but he did not simplify further to remove the coefficient of l.

Hence, the complete solution is given by:

`l=(P-2w)/(2)\\\\l=(P)/(2)-(2w)/(2)\\\\l=(P)/(2)-w`