Respuesta :

We have two similar right angled triangles and each has the base x/2.

Using the Pythagoras theorem we can find the value of x/2 and thus the value of x. The hypotenuse is 10, perpendicular is 8 and base is x/2. So using the theorem we can write:

[tex]10^{2}=8^{2}+( \frac{x}{2})^{2} \\ \\ 100=64+ ( \frac{x}{2})^{2} \\ \\ 36=( \frac{x}{2})^{2} \\ \\ 6=( \frac{x}{2}) \\ \\ x=12[/tex]

Thus the length of side x is 12. Option C is the correct answer.



IsrarAwan
The correct answer is (C) 12

Explanation:
As it is an isosceles triangle and you can see it is divided into two right angled triangle, therefore, we can use Pythagoras theorem here:

[tex]10^2 = 8^2 + ( \frac{x}{2})^2 \\ 100 = 64 + x^2/4 \\ x = \sqrt{144} = 12 [/tex]

NOTE: (x/2) because the triangle base is divided into two halves.

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