Equation Solving Fun
Problem 1
You are given the rectangle below. Find its dimensions (length and width) if the
perimeter of the rectangle is 108 cm. (Hint: First, find the value of x.)
2x
3x+4
To help us solve this problem, we are going to use a spreadsheet. Your partner
should have the Excel program open on his/her screen.
To solve this problem, we want to find a value of x that will give us a perimeter of
108 cm when it is plugged in. Thus, on the spreadsheet, type x in cell A1 and
Perimeter in cell A2. (You have just labeled the two columns.)
Next, we want to fill in some possible values for x. (Do you think that x will be a
large or small number?) To do this, let’s type the number 1 in cell A2. In cell A3,
enter the formula: =A2+1. Now copy this formula and paste it down the A column
to row 15. (Please consult with a friend if you have forgotten how to do this.)
In cell B2, we want to enter a formula for the perimeter. To do this, let’s first think
about how we find the perimeter. (I hope you are all thinking, “You just add up the
sides.”) So. . .
2x + 3x + 4 + 2x + 3x + 4 = 10x + 8 (combine like terms)
Since our values for x begin in cell A2, our formula becomes: =10*A2+8
Please enter this formula in cell B2. Then copy the formula and paste it down the B
column.
Look at your results on the spreadsheet. When the perimeter is 108, x = _________.
Now look back at the original picture of the rectangle. If x = ________, what are the
dimensions of the rectangle?
Width = __________
Length = __________
How did you find these answers?
Is there a way that you could have found x without using the spreadsheet. If so,
show your method in the space below.
Now you try a problem. If you wish, you may use the same spreadsheet, but move
over to columns D and E. (Don’t forget to change your formulas accordingly.) Or,
you may solve the problem algebraically, but don’t forget to show your work below.
When you have finished, you and your partner should save this page and the
spreadsheet with your last names and turn these in to the Homework Dropbox.
Problem 2
You are given the rectangle below. Find its dimensions (length and width) if the
perimeter of the rectangle is 22 ft. (Hint: First, find the value of x.)
5x -11
2x+1
x = __________
width = __________
length = __________