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The Varners live on a corner lot. Often, children cut across their lot to save walking distance. The children’s path is represented by a dashed line. Approximate the walking distance that is saved by cutting across their property instead of walking around the lot. Hypotenuse: 32 ft , Short leg: x , Long leg: x+6

Respuesta :

Answer:

[tex]x= \sqrt{503}-3[/tex]

Step-by-step explanation:

Hypotenuse = 32 feet

Short leg = x

Long leg = x+6

We will use Pythagoras theorem

[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]

[tex]32^2=x^2+(x+6)^2[/tex]

[tex]1024=x^2+x^2+36+12x[/tex]

[tex]2x^2+12x-988=0[/tex]

[tex]x=-3-\sqrt{503}, \sqrt{503}-3[/tex]

Since the distance cannot be negative

So,[tex]x= \sqrt{503}-3[/tex]

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