find the width and length of the playground when you are given the perimeter

Question

Mr. Smith is building a rectangular playground in his backyard for his children. The length of the playground is 5 feet less than triple the width. The perimeter of the playground is 54 feet.

a) Which equation can be used to determine the width of the playground, w, in feet?

(A) w + w – 5 = 54

(B) w + 3w – 5 = 54

(C) 2w + 2(w – 5) = 54

(D) 2w + 2(3w – 5) = 54

b) What is the width of the playground? What is the length of the playground?

c) A square shaped sandbox has a perimeter of 28 feet. Can it fit somewhere within the playground? Explain your answer.

Answer 1

Hi, Gaby.

Okay, so let's call the width, w.

Then, as stated, the length (l) = 3 times the width minus 5. (3w - 5)

Also, the perimeter is 54 feet.

Well, the equation of the perimeter of a rectangle is 2l + 2w

So, we can find the length and width by solving the equation:

2w + 2l = 54

2w + 2(3w - 5) = 54

So, for question (a), the answer is (D).

2w + 6w - 10 = 54

8w - 10 = 54

8w = 64

w = 64/8 = 8 feet

So, if the width is 8 feet, then the length is 3w - 5 = 3(8) - 5 = 19 feet

For problem (b):

So, the width is 8 feet

the length is 19 feet

For problem (c), the question is can a square shaped sandbox of perimeter 28 feet fit inside:

If the sandbox is square, then 4 times the length of the sides = 28

4l = 28

l = 7 feet

So, the length of the sandbox is 7 feet. Since 7 feet is smaller than the shortest side of the playground, the sandbox can fit inside.

So, for (c) the answer is yes.