Question

A new Community Wellness Complex is being built in Oak Valley. The perimeter of the rectangular playing field is 284 yards. The length of the field is 5 yards less than double the width. What are the dimensions of the playing​ field?

Answer 1

To solve this problem, we need to remember that the perimeter of a rectangle can be found using the formula: P = 2 (l + w) where the variable l represents the length of the rectangle and the variable w represents the width of the rectangle.

We know that the length of the field is 5 yards less than double the width, or 2w-5.  We can substitute this value into our formula for the variable l (length).

P = 2 (w + 2w - 5)

Now, we can substitute the value for the perimeter (284) into the equation for the variable p.

284 = 2 (w + 2w - 5)

Next, we should simplify what is inside the parentheses by adding together the like terms.

284 = 2(3w - 5)

Next, we should divide both sides of the equation by 2.

142 = 3w - 5

After that, we can add 5 to both sides of the equation.

147 = 3w

Finally, we should divide both sides of the equation by 3 to get the variable w alone on the right side of the equation.

w = 49

Therefore, the width of the rectangle is 49.  We know that the length is 5 yards less than double the width, or 2w - 5.  To solve for the length, we should substitute in our value for the width and simplify.

l = 2w - 5

l = 2(49) - 5

l = 98 - 5

l = 93

Therefore, the width of the rectangle is 49 yards and the length of the rectangle is 93  yards.

Hope this helps!