A rectangle is four times as long as it is wide. If it has an area of 36 square inches, what are the dimensions?

Question

I have no clue how to start or solve this problem.

Answer 1

I'm going to assume you know that the area of a square is base x height, or alternatively length x width.

 

A good place to start is to take your pencil and draw the rectangle in question.  After you've drawn it, label the sides (a and b or whatever you want), and put down the information you know about the sides.  

 

You know that side 'a', the length, is equal to 4 x the width, 'b', so 'a' = 4'b'.  Now, if you multiply the side lengths together, you'll get the area, 'axb', or, using that information from above, 4bxb, or 4b^2.

 

Since the area is going to be 36, you set the two areas equal to each other: 4b^2=36.  Then solve the equation using algebra.  You should take the square root of both sides first, so you have sqrt(4b^2)=sqrt(36), or 2b=6.  From there, divide both sides by 2, and you get b=3.  You now have side length b!

 

Now, go back to your first equation, a=4b, and use the new information that b=3 to find a.  You should get a=4(3)=12, so a=12, and b=3.

 

For a shortcut to this problem, or a handy way to check your work, you should see that 36 = 6^2.  Then it's just a matter of finding whole factors of 36 that satisfy the rest of the problem.  Start with 2 and 18, and you see that 18 isn't 4x2.  Then go for your next set of factors, 3 and 12.  Tada!  3x4=12, and you have your answer.

Answer 2

Hi Taylor, let x represent the width. Then 4x would represent the length. The area is 36 in².

 

Area of a rectangle:

 

A = L * W

 

L = 4x

 

W = x

 

A = 36 in²

 

Substitute and solve:

 

x * 4x = 36

 

4x² = 36

 

Divide both sides by 4

 

x² =9

 

Find the square root of 9:

 

x = ± 3

 

Solution:

 

x = 3, and x = -3

 

We can discard the solution, x = -3, because the width must be greater than zero.

 

The width is 3 inches.

 

The length is 4 * x, or 4 * 3 = 12. 

 

The length is 12 inches.

 

Check:

 

L * W = 36

 

12 * 3 = 36

 

36 = 36, values check.

 

Questions?

Answer 3

Taylor,

Here's one approach to this problem. We know that the area formula of a rectangle is A = l x w and in this case, our A = 36in². We also know that this rectangle's length is four times its width, so l = 4w, so let's do a little substitution.

 

36in² = 4w x w

 

36in² = 4w²

 

9in² = w²

 

3in = w   so l = 4w = 4(3in) = 12 in

 

Width is 3 inches, and length is 12 inches.

 

Hope this helps!

 

Neal