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)}/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
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