I need help with 1 question please. thank you.

Hello!

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

Use the Pythagorean Theorem for triangle HPF

[tex] PF^{2} + PH^{2} =22^{2} [/tex]

Square the number

[tex]PF^{2} + PH^{2} = 484[/tex]
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Use Pythagorean Theorem for triangle PHL

[tex] PL^{2} = PH^{2} - HL^{2} [/tex]

Put in HL

[tex]PL^{2} = PH^{2} - 4^{2}[/tex]

Square the number

[tex]PL^{2} = PH^{2} - 16[/tex]
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Use the Pythagorean Theorem for triangle PLF

[tex]PL^{2} = PF^{2} - FL^{2} [/tex]

Put in FL

[tex]PL^{2} = PF^{2} - 18^2 [/tex]

Square the number

[tex]PL^{2} = PF^{2} - 324 [/tex]
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Since PL^2 is equal to the two equations we made we know they are equal to each other

[tex]PH^{2} - 16 = PF^{2} - 324[/tex]

Add 16 to both sides

[tex] PH^{2}  = PF^{2} - 308[/tex]

Subtract PF^2 from both sides

[tex] PH^{2} - PF^{2} =  -308[/tex]
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Now we have to equations with the same 2 variables

[tex] PH^{2} - PF^{2} =  -308[/tex]
[tex]PF^{2} + PH^{2} = 484[/tex]

[tex] PF^{2} - 308 + PF^{2} = 484[/tex]

Combine like terms

[tex] 2PF^{2} - 308  = 484[/tex]

Add 308 to both sides

[tex] 2PF^{2}  = 792[/tex]

Divide both sides by 2

[tex] PF^{2}  = 396[/tex]

Take the square root of both sides

[tex]PF = 6 \sqrt{11} [/tex]

The distance between the park to the football field is [tex]6 \sqrt{11} [/tex]

The only choice with that is C

The answer is C

Hope this helps!