Question

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find the value of x. leave your answer in simplest radical form.
answer attempt 1 out of 2
x =

Explanation:

Step1: Find the length of the rectangle's side

Use the Pythagorean theorem for the right - angled triangle at the top:

$$\begin{align*} \text{Length of the base}&=\sqrt{6^{2}+6^{2}}\\ &=\sqrt{36 + 36}\\ &=\sqrt{72}\\ &=6\sqrt{2} \end{align*}$$

Step2: Find the value of \(x\)

Use the Pythagorean theorem for the rectangle (where the diagonal is \(10\) and one side is \(6\sqrt{2}\)):

$$\begin{align*} x&=\sqrt{10^{2}-(6\sqrt{2})^{2}}\\ &=\sqrt{100-72}\\ &=\sqrt{28}\\ &=2\sqrt{7} \end{align*}$$

Answer:

\(2\sqrt{7}\)