Ask Question
14 September, 06:56

A walkway is being installed around a rectangular playground. The playground is 30 feet by 12 feet, and the total area of the playground and the walkway is 1,288 ft^2. What is the width of the walkway?

+3
Answers (2)
  1. 14 September, 07:12
    0
    Answer: the width of the walkway is 8 feet.

    Step-by-step explanation:

    Let x represent the width of the walkway.

    If the length of the playground is 30 feet, then the total length of the playground and the walkway is 30 + x + x = 30 + 2x

    If the width of the playground is 12 feet, then the total width of the playground and the walkway is 12 + x + x = 12 + 2x

    If the total area of the playground and the walkway is 1,288 ft^2, it means that

    (30 + 2x) (12 + 2x) = 1288

    360 + 60x + 24x + 4x² = 1288

    4x² + 84x + 360 - 1288 = 0

    4x² + 84x - 928 = 0

    Dividing through by 4, it becomes

    x² + 21x - 232 = 0

    x² + 29x - 8x - 232 = 0

    x (x + 29) - 8 (x + 29) = 0

    x - 8 = 0 or x + 29 = 0

    x = 8 or x = x = - 29

    Since the width of the walkway cannot be negative, then x = 8
  2. 14 September, 07:19
    0
    10.3

    Step-by-step explanation:

    From these question, we can illustrate the playground has a small rectangle with 30x12ft

    the walkway is around it with an area of 1288ft²

    the playground area = 30 x 12 = 360ft²

    the length dimension of the walkway is 30+y+y (these is because the walkway is round the playground in two sides) = 30 + 2y

    the breadth dimension of the walkway is 12+y+y (these is because the walkway is round the playground in two sides) = 12+2y

    Area of walkway = (30+2y) (12+2y) = 30 (12+2y) + 2y (12+2y) = 360+60y+24y+4y² = 360+84y+4y²

    The total area = 1288ft²

    The total area = area of walkway - area of playground

    1288ft² = 360+84y+4y² - 360

    choose like terms

    1288 = 360-360+84y+4y²

    1288 = 84y+4y²

    divide by 4

    322 = 21y+y²

    y²+21y-322 = 0

    using quadratic formula

    x = (-b±√b²-4ac) / 2a = {-21±√21²-4 (1) (-322) }/2x1 = {-21±√441+1288}/2x1 = - 21±√1729/2

    -21+√1729/2 - 21-√1729/2

    √1729 = 41.5812457726

    -21+√1729/2 - 21-√1729/2

    {-21+41.5812457726}/2 {-21-41.5812457726}/2

    20.5812457726/2 - 62.5812457726/2

    10.2906228863 - 31.2906228863

    we disregard the negative sign

    our width is 10.2906228863 ≅10.3
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “A walkway is being installed around a rectangular playground. The playground is 30 feet by 12 feet, and the total area of the playground ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers