Question

1. solve for x

(right triangle with right angle, two legs marked as equal, hypotenuse 8, one leg labeled x)

1. solve for x

(partial trapezoid or other figure with x, 7sqrt... )

Explanation:

Step1: Identify Triangle Type

The triangle is right - angled and has two equal sides (marked with ticks), so it's an isosceles right - triangle. Let the legs be of length \(x\) (since both legs are equal in an isosceles right - triangle) and the hypotenuse is 8.

Step2: Apply Pythagorean Theorem

For a right - triangle, the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs and \(c\) is the hypotenuse. Here, \(a = x\), \(b = x\) and \(c = 8\). So we have the equation \(x^{2}+x^{2}=8^{2}\).
Simplify the left - hand side: \(2x^{2}=64\).
Divide both sides by 2: \(x^{2}=32\).
Take the square root of both sides: \(x=\sqrt{32}\). Simplify \(\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}\).

Answer:

\(x = 4\sqrt{2}\)