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

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 and the walkway is 1,288 ft^2. What is the width of the walkway?

in progress 0
Kylie 1 week 2021-11-21T11:40:03+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-11-21T11:41:34+00:00

    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

    0
    2021-11-21T11:41:46+00:00

    Answer:

    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)}/2×1 =  {-21±√441+1288}/2×1  = -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

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )