Question

find the value of x. write your answer in simplest form.
x = \square

Explanation:

Step1: Identify the triangle type

The triangle is a right - isosceles triangle (both legs are \(5\sqrt{2}\)), so we can use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = b=5\sqrt{2}\) and \(c=x\).

Step2: Apply the Pythagorean theorem

Substitute \(a = 5\sqrt{2}\) and \(b = 5\sqrt{2}\) into the formula:

$$
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Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{100} = 10\) (we take the positive root since \(x\) represents the length of a side).

Answer:

\(10\)