Answer:
B) [tex]x = \sqrt{60}[/tex]
Step-by-step explanation:
1. As you can see from the image, there are two right triangles in the isosceles triangle. The base of each right triangle is 2 (because 4 ÷ 2 = 2), and the hypotenuse is 8.
2. Let's use Pythagorean Theorem to find the height of each right triangle, which will also give us the height of the isosceles triangle: [tex]a^2 + b^2 = c^2[/tex], where a = height, b = base, and c= hypotenuse.
- [tex]a^2 + 2^2 = 8^2[/tex]
- [tex]a^2 + (2*2) = (8*8)[/tex]
- [tex]a^2 + 4 = 64[/tex] (Simplify both sides of the equation)
- [tex]a^2 + 4 - 4 = 64 - 4[/tex] (Subtract 4 from both sides)
- [tex]a^2 = 60[/tex]
- [tex]\sqrt{a^2} = \sqrt{60}[/tex] (Take square root of both sides
- [tex]a = \sqrt{60}[/tex]
3. The√(60) is the height of each right triangle, and it's also the height of the isosceles triangle. Therefore, the answer is B) x = √60.
