Question

I need help with 1 question please. thank you.

Answer 1

Hello!

let P = park
let F = Football field
let H = Home
let L = library

Use the Pythagorean Theorem for triangle HPF


`PF^(2) + PH^(2) =22^(2)`

Square the number


`PF^(2) + PH^(2) = 484`
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Use Pythagorean Theorem for triangle PHL


`PL^(2) = PH^(2) - HL^(2)`

Put in HL


`PL^(2) = PH^(2) - 4^(2)`

Square the number


`PL^(2) = PH^(2) - 16`
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Use the Pythagorean Theorem for triangle PLF


`PL^(2) = PF^(2) - FL^(2)`

Put in FL


`PL^(2) = PF^(2) - 18^2`

Square the number


`PL^(2) = PF^(2) - 324`
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Since PL^2 is equal to the two equations we made we know they are equal to each other


`PH^(2) - 16 = PF^(2) - 324`

Add 16 to both sides


`PH^(2)  = PF^(2) - 308`

Subtract PF^2 from both sides


`PH^(2) - PF^(2) =  -308`
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Now we have to equations with the same 2 variables


`PH^(2) - PF^(2) =  -308`

`PF^(2) + PH^(2) = 484`


`PF^(2) - 308 + PF^(2) = 484`

Combine like terms


`2PF^(2) - 308  = 484`

Add 308 to both sides


`2PF^(2)  = 792`

Divide both sides by 2


`PF^(2)  = 396`

Take the square root of both sides


`PF = 6 √(11)`

The distance between the park to the football field is
`6 √(11)`

The only choice with that is C

The answer is C

Hope this helps!