Michelle's Room: Answer Bolded Question Pls

Question

Michelle is measuring the dimensions of her living room so she can install new flooring. She measures the length at 4√12 feet with her radical tape measure and then measures the width at 3√8 feet. 1. Determine the area of the living room. Leave your answer as a simplified radical expression and include units. 2. Michelle decided she only wants to cover ¾ of the room in the new flooring. Determine the area of flooring she will need to cover ¾ of the room. Leave your answer as a simplified radical expression and include units. 3. For the remaining portion of the living room not covered by the new flooring, Michelle wants to paint the concrete. After carefully measuring the exposed concrete, she determines 6 square feet are already painted and the remaining unpainted area forms a square with side length x. The entire area of concrete, including the painted and unpainted portions, is a total of 31 square feet. Write an equation that could be used to find the unpainted square side length x. 4. After installing the new flooring, Michelle plans to install new baseboards around the perimeter of the room. Help Michelle by determining the perimeter of the room, leaving your answer as a simplified radical expression. 5. When Michelle goes to the local hardware store to purchase the baseboards, the shop owner tells her his conversion calculator is broken and he only has 14 yards of baseboard in stock. Help Michelle by converting the perimeter to yards and determine if the hardware store has enough baseboard for her room. Hint: 3 feet are in 1 yard. Algebra 1B 66502 Unit 08 – Lesson 1-4 Graded Assignment #12 University of Texas at Austin UT High School 2 Part 2 (10 points per question) Michelle decides she is going to cover only half of her living room with the new flooring, and paint the other half, meaning she will cover only 24√6 square feet with the new flooring. 1. After carefully measuring the exposed concrete, she determines 6 square feet are already painted and the remaining unpainted area forms a square with side length x. The entire area of concrete, including the painted and unpainted portions, is a total of 55 square feet. Michelle determines the equation x 2 + 6 = 55 would help determine the side length x of the square she needs to paint. Is Michelle’s equation correct? Explain your reasoning. 2. Solve Michelle’s equation by completing the square and the square root method. What is the side length x of the square to be painted? Be sure to include units in your answer. 3. Juan comes over to help Michelle with his handy room scanner. The room-scanner device is designed to scan an area and give the user the exact dimensions. When Juan scans the area Michelle is not covering with new flooring, the room-scanner gives him an ERROR message and reads out AREA –2x 2+15x+1. Juan isn’t sure how that helps Michelle and he needs your help determining if this equation can be solved for an x value close to what Michelle got by solving her equation. Solve Juan’s equation from the room scanner using the quadratic formula. Be sure to leave your answer as a simplified radical expression and include units. 4. Convert Juan’s value of x for the side length of the square to a decimal and compare it to the value you determined in #2. Is Juan’s room-scanner close to the value of x Michelle’s equation produces?

5. When Michelle goes to buy her flooring, the flooring specialist only sells flooring in bulk quantities measuring √55 feet long by √66 feet wide. Write these dimensions as rational exponents and then determine if the area of the bulk quantity will cover a square with a side length of 8 feet.

Answer 1

55^1/2 Long

66^1/2 Wide

The area to cover is 8 x 8 = 64 square feet. Expressed as a square root that's (64*64)^1/2.

Estimate: It will not be enough. 66 is only 2 larger than 64, and 55 is 9 smaller.

Exact:

64*64 = 4096, so the area to cover is 4096^1/2

55 * 66 = 3630, so the bulk quantity covers an area of 3630^1/2

It's not enough to cover the 8 x 8 floor.