Question

1. a cement path consists of six equal - sized cement squares arranged in a row to form a rectangle. if the total area of the path is 96 square feet, what is the length in feet of the path?

feet

1. a photo collage consists of seven equal - sized square photos arranged in a row to form a rectangle. if the total area of the collage is 567 square inches, what is the length of the collage?

inches

Explanation:

Step1: Find area of one square

Let the side - length of each square be $x$. For the cement path with 6 squares and total area $A = 96$ square feet, the area of one square is $a=\frac{96}{6}=16$ square feet.

Step2: Find side - length of one square

Since the area of a square is $a = x^{2}$, and $a = 16$, then $x=\sqrt{16}=4$ feet.

Step3: Find length of the path

The length of the path (formed by 6 squares in a row) is $L = 6x$. Substituting $x = 4$ feet, we get $L=6\times4 = 24$ feet.

For the photo - collage:

Step1: Find area of one square

Let the side - length of each square photo be $y$. For the photo collage with 7 squares and total area $A'=567$ square inches, the area of one square is $a'=\frac{567}{7}=81$ square inches.

Step2: Find side - length of one square

Since the area of a square is $a'=y^{2}$, and $a' = 81$, then $y=\sqrt{81}=9$ inches.

Step3: Find length of the collage

The length of the collage (formed by 7 squares in a row) is $L'=7y$. Substituting $y = 9$ inches, we get $L'=7\times9 = 63$ inches.

Answer:

1. 24
2. 63