Sally's bedroom dimensions are depicted in the figure below. If she is planning on hanging lights around the perimeter of her room, how many feet of lights does she need to purchas... Sally's bedroom dimensions are depicted in the figure below. If she is planning on hanging lights around the perimeter of her room, how many feet of lights does she need to purchase?

Understand the Problem
The question describes Sally's bedroom dimensions in a diagram. We are given one side as 8 ft and the diagonal as 17 ft. Sally wants to hang lights around the perimeter, so the goal is to find the total length of the lights needed, which is the perimeter of the room. We need to determine the length of the unknown side of the rectangle using the Pythagorean theorem, then calculate the perimeter.
Answer
46
Answer for screen readers
46
Steps to Solve
- Find the unknown side length
Using the Pythagorean theorem, where the diagonal is the hypotenuse $c$, and the known side is $a$, we can find the unknown side $b$. $a^2 + b^2 = c^2$
- Substitute the given values
Substitute $a = 8$ and $c = 17$ into the Pythagorean theorem: $8^2 + b^2 = 17^2$
- Solve for $b$
Simplify and solve for $b$: $64 + b^2 = 289$ $b^2 = 289 - 64$ $b^2 = 225$ $b = \sqrt{225}$ $b = 15$
- Calculate the perimeter
The perimeter of a rectangle is given by $P = 2(l + w)$, where $l$ is the length and $w$ is the width. In this case, $l = 15$ and $w = 8$. $P = 2(15 + 8)$ $P = 2(23)$ $P = 46$
46
More Information
The perimeter of Sally's room is 46 feet, which means she needs to purchase 46 feet of lights.
Tips
A common mistake is to add all the numbers given in the problem without considering that the diagonal is not a side of the rectangle and cannot be used to calculate the perimeter directly. Also, forgetting to multiply by 2 when calculating the perimeter is a common mistake.
AI-generated content may contain errors. Please verify critical information