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? Show your work.

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

Answer 1

for a) the answer is choice D

write two equations:

L = 3W-5 (5 feet less than triple the width)

P = 2W + 2L (definition)

substitute L into the P equation, and replace P with 54 (given)

2w + 2(3w – 5) = 54

for b) we just solve the equation we just developed for part a) for the variable w

2w + 6w -10 = 54

8w - 10 = 54

8w = 64

w= 8

to solve for length use your perimeter equation and the width you just determined

P = 2w+2L

54 = 2(8) +2L

solve for L

38 = 2L

L = 19

for part c) the perimeter is close half of the original. Since the perimeter is smaller, the area will also be smaller, therefore it will fit