Question

6. Multiselect A square room has side lengths
that can be represented by the expression
6x3 feet. Kyra wants to cover the floor in
square tiles with side lengths that can be
represented by the expression 3x feet.
(Lesson 3)

A. Which of the following statements are
correct? Select all that apply.
The area of one tile is 3x2 ft2.

1.The area of one tile is 9x2 ft2.

2.The area of the floor is 36x3 ft?.

3.The area of the floor is 18x4 ft2.

4.The area of the floor is 36x6 ft2.

B. If x= 3, then what number of tiles will be
needed to cover the floor?

Answer 1

The area of a square and a rectangle is given by multiplying the lengths of the sides of the square

A. The correct statements are;

The area of one square tiles 9·x²

The area of the floor is 36·x⁶

B. The number of tiles needed to cover the floor 324 tiles

The reason the above values are correct are as follows:

A. The given parameters are;

The expression that represents the side lengths of the square room = 6·x³ feet

The side lengths of the square tiles = 3·x

Required:

To select the correct expressions

Solution:

The area of one square tiles = 3·x × 3·x = 9·x²

The area of the floor = 6·x³ × 6·x³ = 36·x⁽³ ⁺ ³⁾ = 36·x⁶

B. If x = 3, we have;

$The \ number \ of \ tiles = \dfrac{Area \ of \ floor}{Area \ of \ a \ tile}$

The area of the floor, = 36×3⁶ = 26,244

The area of one tile = 9 × 3² =  81

$The \ number \ of \ tiles = \dfrac{26,244}{81} = 324$

The number of tiles needed to cover the floor = 324 tiles

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