perimeter is 28 feet. the length is one foot less than 4 times the width. what is the length and width?

Answer 1

Hello Joan,

Since the length and width differ in units of measure, the problem tells us we are dealing with a rectangle.

The formula for determining the perimeter of a rectangle - something we must use to solve this problem is as follows:

P = 2(L + W) or P = 2(L) + 2(W) where P equals the perimeter, L equals the length, and W equals the width. You will notice that the second formula is exactly the same as the first due to the distributive law of math being applied. I prefer the second equation, therefore that is the one we will use.

Next, we need to develop some expressions which represent the length and width adhering to the specifications of the problem. Therefore, according to the problem:

Let x equal the width and,

Let 4x -1 equal the length.

Next, we want to substitute the expressions we just came up with in the formula. Therefore:

P = 2(L) + 2(W)

28 = 2 (4x - 1) + 2 (x) <-----Now solve the equation

28 = 8x - 2 + 2x <-----Combine like terms

28 = 10x - 2 <-----Add two to both sides of equation

30 = 10x <------Divide both sides by 10

x = 3 <------This is the width

The length is 4(x) - 1 so we now substitute 3 for x to determine the length. Therefore:

4(x) - 1

4(3) -1 =

12 - 1 =

11 <------This is the length.

Finally, we need to check our work. To do so, we want to substitute the values of 3 for the width, and 11 for the length to ensure it equals 28.

P = 2(L) + 2(W)

28 = 2(11) + 2(3)

28 = 22 + 6

28 = 28

The numbers check and therefore, the solution is valid. If you need any further clarity on the solution I provided, simply press "Add Comment" and the question will appear beneath the solution. Please feel free to provide any feedback or ask any further questions if needed. Best!