Question

use your notes in your packet to show work. set up the problem. ² + ² = ² solution x = cm (rounded to the nearest hundredths.)

Explanation:

Step1: Apply Pythagorean theorem

$$x^{2}+6.5^{2}=8.5^{2}$$

Step2: Rearrange to solve for \(x\)

$$x^{2}=8.5^{2}-6.5^{2}$$
$$x^{2}=(8.5 + 6.5)(8.5 - 6.5)$$ (using \(a^{2}-b^{2}=(a + b)(a - b)\))
$$x^{2}=15\times2$$
$$x^{2}=30$$

Step3: Calculate \(x\)

$$x=\sqrt{30}\approx5.48$$

Answer:

Set up the problem: \(x^{2}+6.5^{2}=8.5^{2}\)
Solution \(x = 5.48\) cm