The perimeter of a local dog park measures 156ft

Question

The perimeter of a local dog park measures 156ft. If the length of the park is 2 ft less then 3x the width what are the dimensions of the park?

Answer 1

Hi David,

 

Let's begin by assigning letters to represent our two unknowns:

    L = length of dog park

    W = width of dog park

 

Since we have two unknowns, let's see if we can express one unknown in terms of the other.  We are told that the length is 2 feet less than 3 times its width.  We can write this algebraic expression to reflect this verbal statement:

    L = 3W - 2 (three times width minus two)

 

Now let's recall the perimeter formula for a rectangle:

    P = 2L + 2W

 

We can replace L with 3W - 2 and plug in 156 (given perimeter) for P and then solve the formula equation for W:

    156 = 2(3W - 2) + 2W

    156 = 6W - 4 + 2W

    156 = 8W - 4

    8W = 156 + 4

    8W = 160

      W = 160/8

      W = 20 feet (width of dog park)

 

Now we plug in 20 for W in our expression for L in terms of W and solve for L:

      L = 3(20) - 2

      L = 60 - 2

      L =58 feet (length of dog park)

 

Finally, we can verify that our answers for L and W are correct by plugging their values into the perimeter formula and see if the perimeter matches the given value of 156:

     2(58) + 2(20) = 116 + 40 = 156 (correct)

 

So our verification is successful and we know that we have the right values for the dimensions of the dog park.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.