Module Two Discussion Question:

Solve the problem below. For your initial post in Brightspace, copy the description of your rectangle given in the box below and then enter your solution to all four parts (parts a, b, c, and d) of the problem. To copy the description of your rectangle, highlighting and using "copy" from here in Mobius and then using "paste" into Brightspace should work.

A rectangle has perimeter128 cm and its length is 1 cm more than twice its width.

Find the dimensions of a rectangle given that its perimeter is 128 cm and its length is 1 cm more than twice its width.

Set up your solution using the variables for the length, for the width, and for the perimeter.

Part a: Using the definition of perimeter, write an equation forin terms ofand.

Part b: Using the relationship given in the problem statement, write an equation forin terms of.

Solve the equations from parts a and b.

Part c: The width is ___ cm.

Part d: The length is ___ cm.

Feedback

In your Discussion post, don't just post your final answer. It's very important that you explain to your classmates how you arrived at that answer.

It helps to start by choosing good names for the variables. It would make sense here to havebe the Length of the rectangle,be the Width of the rectangle, andbe the Perimeter of the rectangle.

Part a: How isrelated toand? To measure the perimeter, you need to go down one length, across one width, back one length, and back one width. Write that as an equation forin terms of and. This is your answer to part a.

Part b: You should continue to use the information given in the question. The length is1more than twice the width - write that as an equation forin terms of. This is your solution to part b.

Your equation from part a has 3 variables (,and)and you'd like to reduce it to 2 variables. You're told thatP=128. You can put that into your perimeter equation for.

Now the perimeter equation has 2 variables (and)and you'd like to reduce it to 1 variable. Use your equation from part b to replace.

Now the perimeter equation hasonly 1 variable () left!

Parts c and d: Solve the equation forand use your answer to calculate.