Question

lesson 8: which variable to solve for? (part 1) cool down: a rectangular relationship the perimeter of a rectangle is 48 centimeters. the relationship between the length, the width, and the perimeter of the rectangle can be described with the equation 2·length + 2·width = 48. find the length, in centimeters, if the width is: 1. 10 centimeters 2. 3.6 centimeters 3. w centimeters

Explanation:

Step1: Recall perimeter formula

Let length be $l$ and width be $w$. The perimeter formula is $2l + 2w=48$. We can simplify it to $l + w = 24$ (dividing both sides of $2l + 2w = 48$ by 2).

Step2: Solve for length when $w = 10$

Substitute $w = 10$ into $l+w = 24$. Then $l=24 - w$. So $l=24 - 10=14$ centimeters.

Step3: Solve for length when $w = 3.6$

Substitute $w = 3.6$ into $l + w=24$. Then $l=24 - w$. So $l=24 - 3.6 = 20.4$ centimeters.

Step4: Solve for length when $w$ is a variable

Substitute $w$ into $l + w=24$. Then $l=24 - w$ centimeters.

Answer:

1. 14 centimeters
2. 20.4 centimeters
3. $(24 - w)$ centimeters