To solve the problems using the Pythagorean Theorem, we use the formula:
\[
a^2 + b^2 = c^2
\]
where:
- \( a \) and \( b \) are the lengths of the two legs of the right triangle,
- \( c \) is the length of the hypotenuse.
We will solve each problem step by step.
---
Problem 1:
Given:
- One leg \( a = 9 \)
- The other leg \( b = 12 \)
- Hypotenuse \( c = x \)
Using the Pythagorean Theorem:
\[
a^2 + b^2 = c^2
\]
\[
9^2 + 12^2 = x^2
\]
\[
81 + 144 = x^2
\]
\[
225 = x^2
\]
\[
x = \sqrt{225}
\]
\[
x = 15
\]
Answer:
\[
\boxed{15}
\]
---
Problem 2:
Given:
- One leg \( a = 20 \)
- Hypotenuse \( c = 25 \)
- The other leg \( b = x \)
Using the Pythagorean Theorem:
\[
a^2 + b^2 = c^2
\]
\[
20^2 + x^2 = 25^2
\]
\[
400 + x^2 = 625
\]
\[
x^2 = 625 - 400
\]
\[
x^2 = 225
\]
\[
x = \sqrt{225}
\]
\[
x = 15
\]
Answer:
\[
\boxed{15}
\]
---
Problem 3:
Given:
- One leg \( a = 9 \)
- Hypotenuse \( c = 15 \)
- The other leg \( b = x \)
Using the Pythagorean Theorem:
\[
a^2 + b^2 = c^2
\]
\[
9^2 + x^2 = 15^2
\]
\[
81 + x^2 = 225
\]
\[
x^2 = 225 - 81
\]
\[
x^2 = 144
\]
\[
x = \sqrt{144}
\]
\[
x = 12
\]
Answer:
\[
\boxed{12}
\]
---
Problem 4:
Given:
- One leg \( a = 8 \)
- Hypotenuse \( c = 10 \)
- The other leg \( b = x \)
Using the Pythagorean Theorem:
\[
a^2 + b^2 = c^2
\]
\[
8^2 + x^2 = 10^2
\]
\[
64 + x^2 = 100
\]
\[
x^2 = 100 - 64
\]
\[
x^2 = 36
\]
\[
x = \sqrt{36}
\]
\[
x = 6
\]
Answer:
\[
\boxed{6}
\]
---
Problem 5:
Given:
- One leg \( a = 3 \)
- The other leg \( b = 4 \)
- Hypotenuse \( c = x \)
Using the Pythagorean Theorem:
\[
a^2 + b^2 = c^2
\]
\[
3^2 + 4^2 = x^2
\]
\[
9 + 16 = x^2
\]
\[
25 = x^2
\]
\[
x = \sqrt{25}
\]
\[
x = 5
\]
Answer:
\[
\boxed{5}
\]
---
Problem 6:
Given:
- One leg \( a = 15 \)
- Hypotenuse \( c = 25 \)
- The other leg \( b = x \)
Using the Pythagorean Theorem:
\[
a^2 + b^2 = c^2
\]
\[
15^2 + x^2 = 25^2
\]
\[
225 + x^2 = 625
\]
\[
x^2 = 625 - 225
\]
\[
x^2 = 400
\]
\[
x = \sqrt{400}
\]
\[
x = 20
\]
Answer:
\[
\boxed{20}
\]
---
Final Answers:
\[
\boxed{15, 15, 12, 6, 5, 20}
\]
Parent Tip: Review the logic above to help your child master the concept of pythagorean theorem printable worksheet.
