Answer:
x = 10
Step-by-step explanation:
Given isosceles triangle with legs equal to [tex]\sqrt{74}[/tex] units. The height of 7 units divides this triangle into two congruent right triangles. The height of the isosceles triangle drawn to the base is its median to, so the height divides the base into two equal segments with length of [tex]\frac{x}{2}[/tex] units.
By th Pythagorean theorem,
[tex]\left(\dfrac{x}{2}\right)^2+7^2=(\sqrt{74})^2\\ \\\dfrac{x^2}{4}=74-49\\ \\\dfrac{x^2}{4}=25\\ \\\dfrac{x}{2}=5\\ \\x=2\cdot 5\\ \\x=10\ units[/tex]
