Question

ENVELOPES An office supply company produces yellow document envelopes.

The envelopes come in a variety of sizes, but the length is always 4 centimeters
more than double the width, x.
a. Write a polynomial equation to give the perimeter P of any of the envelopes.
b. Predict the perimeter of an envelope with a width of 6 centimeters.

Answer 1

a. P = 6x + 8

b. P = 44

Explanation:

The formula for the perimeter of a rectangle/envelope is the sum of all the sides which would be the following

P = length + length + width + width

Based on the description we can say that the length is equal to the following arithmetic expression

L = 2x + 4

a. Therefore, now we can plug this value into the Perimeter formula to create a polynomial for it

P = (2x + 4) + (2x + 4) + x + x

P = 6x + 8

b. To find the perimeter of an envelope with a width of 6 we simply need to substitute 6 for x and solve for P using the Polynomial above.

P = 6(6) + 8

P = 36 + 8

P = 44