Question

8 alexa made a square quilt with sides 6 feet long. she wants to sew a border along the edges. how many feet of border material will she need?
9 one dimension of a rectangular yard is 9 m. the area of the yard is 108 m². what is the other dimension?
10 henry is tiling the top of a coffee table. the tabletop measures 36 in. by 18 in. each tile covers 9 in.² how many tiles will henry need?

Explanation:

8.

Step1: Recall the formula for the perimeter of a square

The perimeter of a square is \(P = 4s\), where \(s\) is the side - length of the square.

Step2: Substitute the value of \(s\) into the formula

Given \(s = 6\) feet. Then \(P=4\times6\).

$$P = 24$$

9.

Step1: Recall the formula for the area of a rectangle

The area of a rectangle is \(A=l\times w\), where \(l\) and \(w\) are the length and width of the rectangle. Let one dimension \(l = 9\)m and \(A = 108\)m². We need to find \(w\).

Step2: Solve for \(w\)

We know that \(w=\frac{A}{l}\). Substitute \(A = 108\)m² and \(l = 9\)m into the formula.

$$w=\frac{108}{9}=12$$

10.

Step1: Calculate the area of the table - top

The area of a rectangle \(A=l\times w\). Given \(l = 36\)in and \(w = 18\)in. Then \(A=36\times18\).

$$A = 648$$

in²

Step2: Calculate the number of tiles

Let the number of tiles be \(n\). Each tile has an area of \(a = 9\)in². Then \(n=\frac{A}{a}\). Substitute \(A = 648\)in² and \(a = 9\)in² into the formula.

$$n=\frac{648}{9}=72$$

Answer:

1. \(24\) feet
2. \(12\)m
3. \(72\) tiles