Help with math problem...?

Question

The perimeter of Sportland Park is 624 yd. The length of the rectangular park is 8yd more than 3 times the width. Find the dimensions of the park.

Please tell the steps on how you solved it. Thanks a lot!, my answer isn't matching up with the answers in the back of the book.

Answer 1

To start DRAW A RECTANGLE. Off to the side make a note that the perimeter is 624 yards.  Now how do you solve the perimeter of a rectangle normally?  Well, you add up all the sides (2 widths and 2 lengths - the widths are identical to each other and lengths are identical to each other).  SO WRITE AN EQUATION.

"The length of the rectangular park is 8yd more than 3 times the width."  So we can deduct that LENGTH = 8yd + 3w

And WIDTH = w

So to find the perimeter we need to 2(add up 2 widths and two lengths and set it equal to your perimeter, 624yd like so:

2w + 2(8 + 3w) = 624

2w + 16 + 6w = 624

8w + 16 = 624

.......-16.....-16

8w = 608 (divide by 8 on both sides)

WIDTH = 76yd

But you need to find the DIMENSIONS (so WIDTH AND LENGTH)

Remember that equation in the beginning LENGTH = 8 + 3w?  Well now that we know w, we can plug in 76 into every place we see w and solve for LENGTH.  

8 + 3(76) = 8 + 228 = 236

So, LENGTH = 236yd

And to see if it's correct just use the formula 2(WIDTH) + 2(LENGTH) = PERIMETER

2(76) + 2(236) = 152 + 472 = 624 (THE PERIMETER!)

Hope this helps!