Question

Find the value of x in the isosceles triangle shown below.

Answer 1

Answer:

B) $x = \sqrt{60}$

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: $a^2 + b^2 = c^2$, where a = height, b = base, and c= hypotenuse.

• $a^2 + 2^2 = 8^2$
• $a^2 + (2*2) = (8*8)$
• $a^2 + 4 = 64$ (Simplify both sides of the equation)
• $a^2 + 4 - 4 = 64 - 4$ (Subtract 4 from both sides)
• $a^2 = 60$
• $\sqrt{a^2} = \sqrt{60}$ (Take square root of both sides
• $a = \sqrt{60}$

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.