Respuesta :

greenforestaz

Step-by-step explanation:

step 1. let's call the line in the middle y.

step 2. y = sqrt(5^2 + 7^2) = sqrt(74). pythagorean theorem.

step 3. x^2 + y^2 =100 (pythagorean theorem))

step 4. x^2 + (sqrt(74))^2 = 100.

step 5. x^2 = 100 - 74

step 6. x^2 = 26

step 7. x = sqrt(26). note: sqrt is the square root.

The value of the x is [tex]\sqrt{26}[/tex].

To understand more, check below explanation.

Pythagoras theorem :

Apply Pythagoras theorem in right side triangle,

            Hypotenuse[tex]=\sqrt{5^{2}+7^{2} } =\sqrt{25+49}=\sqrt{74}[/tex]

Now apply Pythagoras theorem in the left side triangle,

              [tex]Hypotenus^{2} +x^{2} =10^{2} \\\\(\sqrt{74} )^{2} +x^{2} =100\\\\x^{2} =100-74=26\\\\x=\sqrt{26}[/tex]

Hence, the value of the x is [tex]\sqrt{26}[/tex].

Learn more about the Pythagoras theorem  here:

https://brainly.com/question/21332040

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