Luffy D.

asked • 29d

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.

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.

Lauren T.

tutor
1. Simplify the radicals: 4 √12 = 4 √(3*4) = 4 * 2 √3 = 8 √3 3 √8 = 3 √(2*4) = 3 * 2 √2 = 6 √2 8 * 6 * √3 * √2 = 48 √6 feet 2. Multiply by 3/4: 48 √6 * (3/4) = (48 * 3/4) √6 = 36 √6 feet 3. Subtraction: √(31-6) = √25 = 5 square feet 4. Multiply radicals from question 1 by 2 and add to find perimeter: (2 * 8 √3) + (2 * 6 √2) = 16 √3 + 12 √2
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29d

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