Answer:
x = 2[tex]\sqrt{5}[/tex]
Step-by-step explanation:
Since the 2 legs are congruent, both 6 then the triangle is isosceles.
The line from the vertex to the base is a perpendicular bisector, dividing the base into 2 parts of 4 units.
Using Pythagoras' identity in one of the right triangles.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
x² + 4² = 6²
x² + 16 = 36 ( subtract 16 from both sides )
x² = 20 ( take the square root of both sides )
x = [tex]\sqrt{20}[/tex] = [tex]\sqrt{4(5)}[/tex] = 2[tex]\sqrt{5}[/tex]
