Understanding Perimeter and Solving for Width

The video tutorial explains how to find the perimeter of a rectangle using the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. It visualizes the rectangle and its sides, then demonstrates how to rearrange the formula to solve for width. The tutorial also explores alternative methods to achieve the same result, emphasizing the flexibility in mathematical problem-solving.

What is the formula for finding the perimeter of a rectangle?

• P = l + w

• P = 2(l + w)

• P = 2l + 2w

• P = l * w

If a rectangle has a length of 5 and a width of 3, what is its perimeter?

• 18

• 20

• 16

• 15

What is the first step in rewriting the perimeter formula to solve for width?

• Add 2l to both sides

• Multiply both sides by 2

• Subtract 2l from both sides

• Divide both sides by 2

After isolating 2w, what is the next step to solve for w?

• Subtract 2 from both sides

• Divide both sides by 2

• Multiply both sides by 2

• Add 2 to both sides

What is the final expression for width when solving P = 2l + 2w?

• w = 2(P - l)

• w = P - 2l

• w = (P - 2l) / 2

• w = P / 2 - l

What is an alternative method to solve for width in the perimeter formula?

• Factoring out a 2

• Subtracting 2 from both sides

• Multiplying both sides by 2

• Adding 2 to both sides

How can the expression P = 2(l + w) be simplified to solve for w?

• Subtract l from both sides

• Multiply both sides by 2

• Divide both sides by 2

• Add l to both sides

What is the expression for width when using the alternative method?

• w = 2P - l

• w = P / 2 - l

• w = P / 2 + l

• w = P - 2l

Why are the expressions (P - 2l) / 2 and P / 2 - l equivalent?

• They are not equivalent

• Both expressions simplify to the same value

• One is a factor of the other

• They represent different equations

What is the purpose of dividing both sides of the equation by 2 in the alternative method?

• To subtract 2 from the equation

• To multiply the equation by 2

• To add a coefficient of 2

• To eliminate the coefficient of 2