Question

The width of a rectangle measures (3.1s-1.6)(3.1s−1.6) centimeters, and its length measures (7.2s-4.6)(7.2s−4.6) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle? A. −6.2+10.3s B. −12.4+20.6s C. 1.5s+2.6 D. 5.2+3s

Answer 1

B. -12.4 + 20.6s.

Explanation:

Perimeter = 2*length + 2 * width

= 2(3.1s - 1.6) + 2(7.2s - 4.6)

= 6.2s + 14.4s - 3.2 - 9.2

= 20.6s - 12.4

= -12.4 + 20.6s.

Answer 2

`\boxed{-12+20.6s}`

To find the perimeter of a shape, we add length + width + length + width (or length * 2 + width *2). So we would multiply the width, (3.1s - 1.6), and the length, (7.2s - 4.6), by 2, and then add them together to find the perimeter.

2(3.1s - 1.6) + 2(7.2s - 4.6)

This is equal to:

6.2s + 14.4s - 3.2 - 9.2

Simplified, this is equal to:

20.6s - 12.4

(We have to switch it around, but this answer is equal to option b.)

-12.4 + 20.6s

Tip: To simplify an equation, you add like terms. Like terms are numbers that have the same variables or exponents; for example, -4 and 3 are like terms, as well as 5^2 and 8^2. (Keep in mind, the variables and/or exponents have to be the same if you combine the like terms. Numbers with different variables and exponents can never be combined!)