Question

worksheet the pythagorean theorem find x. 1. triangle diagram 2. triangle diagram 3. triangle diagram 4. triangle diagram 5. triangle diagram 6. rectangle diagram use a pythagorean triple to find x. 7. triangle diagram 8. triangle diagram 9. triangle diagram 10. triangle diagram 11. triangle diagram 12. triangle diagram

Explanation:

Let's solve problem 1 as an example (right - triangle with legs 12 and 9, find hypotenuse \(x\)):

Step 1: Recall Pythagorean Theorem

The Pythagorean Theorem states that for a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here, \(a = 12\), \(b=9\) and \(c = x\). So we have the equation \(12^{2}+9^{2}=x^{2}\).

Step 2: Calculate the squares

Calculate \(12^{2}=144\) and \(9^{2} = 81\). Then the equation becomes \(144 + 81=x^{2}\).

Step 3: Sum the values

\(144+81 = 225\), so \(x^{2}=225\).

Step 4: Take the square root

Take the square root of both sides. Since \(x\) represents the length of a side of a triangle, we take the positive square root. \(\sqrt{x^{2}}=\sqrt{225}\), so \(x = 15\).

Answer:

\(x = 15\)

(If you want solutions for other problems, you can provide more specific problem numbers and we will solve them in a similar way using the Pythagorean Theorem \(a^{2}+b^{2}=c^{2}\) where \(a\) and \(b\) are the legs of the right - triangle and \(c\) is the hypotenuse, or by using Pythagorean triples for problems 7 - 12)