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 = 26. What error did the student make? Complete the explanation. Then solve for l.

A) The student made an algebraic error by subtracting 2w from P instead of isolating l. To solve for l, you should rearrange the formula as l = (P - 2w)/2.
B) The student correctly solved for l by simplifying the formula P - 2w = 26.
C) The student made a conceptual error in understanding how to solve for l in the perimeter formula.
D) The student's approach is valid, but the formula P - 2w = 26 cannot be used to find l.

Answer 1

The student incorrectly subtracted 2w from P and left the answer as P - 2w = 26. The correct method is to subtract 2w from P and then divide by 2 to solve for l, resulting in the formula l = (P - 2w) / 2.

Step-by-step explanation:

The student made an algebraic error when trying to solve for l in the perimeter formula. The correct way to isolate l is by first subtracting 2w from both sides of the equation and then dividing by 2. So the correct formula to find l would be l = (P - 2w) / 2.

Here is how to correct the student's work step-by-step:

1. Start with the formula P = 2l + 2w
2. Subtract 2w from both sides to get P - 2w = 2l
3. Divide both sides by 2 to isolate l, resulting in l = (P - 2w) / 2