Question

A helicopter landing pad has a length of 80 ft and a width of 50 ft. A safety zone

of uniform width, which is not to be entered during landing, surrounds the landing
pad. The landing pad and safety zone together have a combined area of 10800 ft2,
what is the uniform width (safety zone) around the landing pad?

Answer 1

uniform width around the landing pad = 9.41 feet

Explanation:

Length of landing pad = 80 ft

width of landing pad = 50 ft

Length of safety zone = (80 + 2w)

width of safety zone = (50 + 2w)

Total area = 10800
`ft^(2)`

Area of landing pad = length x width

= 80 x 50

= 4000
`ft^(2)`

Area of landing pad = 4000
`ft^(2)`

Thus,

area of safety zone = total area - area of landing pad

= 10800 - 4000

= 6800

area of safety zone = 6800
`ft^(2)`

But,

area of safety zone = length x width

6800 = (80 + 2w) x (50 + 2w)

6800 = 4000 + 160w + 100w + 4
`w^(2)`

divide through by 4,

1700 =
`w^(2)` + 65w + 1000

⇒
`w^(2)` + 65w + 1000 - 1700 = 0

`w^(2)` + 65w -700 = 0

Applying the quadratic formula,

w = (-b ±
`\sqrt{b^(2) -4ac}`) ÷ 2a

a = 1, b= 65 and c = -700

w = (-65 ±
`\sqrt{(65)^(2)-(4*1*-700) }`) ÷ 2

= (-65 ±
`√(7025)`) ÷ 2

= (-65 ± 83.82)÷ 2

w = (-65 + 83.82) ÷ 2 OR (-65 - 83.82) ÷ 2

= 18.82 ÷ 2 OR -148.82 ÷ 2

= 9.41 OR -74.41

Thus, w = 9.41 ft.