Question

Find the length of the third side. If necessary, write in simplest radical form. 10 5

Answer 1

Answer:

x= $5\sqrt{5}$

Step-by-step explanation:

To solve this problem we first observe the Pythagoras equation. If a= 10 and b =5 are the lengths of the legs of a right triangle and c= x is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

This relationship is represented by the formula:

$a^{2} + b^{2} = c^{2}$ =>$10^2 +5 ^2 = x^2$

=> 100 + 25 = $x^2$

=> $\sqrt{125}$ = x => $\sqrt{25} \sqrt{5}$ = x

=> x= 5$\sqrt{5}$