Question

1.Each side of a square has a length of 5x. Use your area expression to find the area of the square when x = 2.2 centimeters. Show your work.
2. A rectangle has a length of 6 and a width of y + 4. Use the distributive property to write an expression to represent the area of the rectangle.

3.A rectangle has a length of 6 and a width of y + 4. Use your area expression to find the area of the rectangle when y = 3 1/2 inches. Show your work.

4. The area of a rectangle is 8w + 18 square feet. The length of the rectangle is 2 feet. Use factoring to write an expression to represent the width of the rectangle.

Answer 1

1. The area is l * w, so just multiply 5x by 5x. Replacing x with 2.2 gets:
(5 * 2.2) * (5 * 2.2)

11 * 11
= 121

So, the area of the square when x = 2.2 centimeters is 121 sq cm.

2. The expression for this equation would be:
6(y + 4)

And using the distributive property on this to get the simplified expression, just multiply both y and 4 by 6.

6 * y + 6 * 4
6y + 24
So, your expression is 6y + 24.

3. For this one, let's make y's value 3.5 instead of 3 1/2 to make it easier to solve.

We just use the above expression to solve.
6 * 3.5 + 6 * 4
21 + 24
= 45

So, the area of the rectangle when y = 3 1/2 is 45 sq in.

4. For this last one, let's use the formula w = A/l to form an expression that will represent the width.

w = 8w + 18/2

Now, let's simplify it by dividing 8w and 18 by 2.
w = 8w/2 + 18/2

w = 4w + 9

So the expression to represent the width of the rectangle is 4w + 9.
Hope this helped!