To solve the problems using the Pythagorean Theorem, we need to identify the right triangles in each shape and apply the theorem. The Pythagorean Theorem states:
\[
a^2 + b^2 = c^2
\]
where \(a\) and \(b\) are the legs of the right triangle, and \(c\) is the hypotenuse.
Let's go through each problem step by step.
---
Problem 1:
The first image shows a right triangle with one leg labeled as 3 units and the other leg labeled as 4 units. We need to find the hypotenuse (\(x\)).
Using the Pythagorean Theorem:
\[
a = 3, \quad b = 4, \quad c = x
\]
\[
3^2 + 4^2 = x^2
\]
\[
9 + 16 = x^2
\]
\[
25 = x^2
\]
\[
x = \sqrt{25}
\]
\[
x = 5
\]
So, the length of the hypotenuse is:
\[
\boxed{5}
\]
---
Problem 2:
The second image shows a right triangle with one leg labeled as 5 units and the hypotenuse labeled as 13 units. We need to find the other leg (\(x\)).
Using the Pythagorean Theorem:
\[
a = 5, \quad b = x, \quad c = 13
\]
\[
5^2 + x^2 = 13^2
\]
\[
25 + x^2 = 169
\]
\[
x^2 = 169 - 25
\]
\[
x^2 = 144
\]
\[
x = \sqrt{144}
\]
\[
x = 12
\]
So, the length of the other leg is:
\[
\boxed{12}
\]
---
Problem 3:
The third image shows a right triangle with one leg labeled as 7 units and the hypotenuse labeled as 25 units. We need to find the other leg (\(x\)).
Using the Pythagorean Theorem:
\[
a = 7, \quad b = x, \quad c = 25
\]
\[
7^2 + x^2 = 25^2
\]
\[
49 + x^2 = 625
\]
\[
x^2 = 625 - 49
\]
\[
x^2 = 576
\]
\[
x = \sqrt{576}
\]
\[
x = 24
\]
So, the length of the other leg is:
\[
\boxed{24}
\]
---
Problem 4:
The fourth image shows a right triangle with one leg labeled as 8 units and the hypotenuse labeled as 17 units. We need to find the other leg (\(x\)).
Using the Pythagorean Theorem:
\[
a = 8, \quad b = x, \quad c = 17
\]
\[
8^2 + x^2 = 17^2
\]
\[
64 + x^2 = 289
\]
\[
x^2 = 289 - 64
\]
\[
x^2 = 225
\]
\[
x = \sqrt{225}
\]
\[
x = 15
\]
So, the length of the other leg is:
\[
\boxed{15}
\]
---
Problem 5:
The fifth image shows a right triangle with one leg labeled as 12 units and the hypotenuse labeled as 20 units. We need to find the other leg (\(x\)).
Using the Pythagorean Theorem:
\[
a = 12, \quad b = x, \quad c = 20
\]
\[
12^2 + x^2 = 20^2
\]
\[
144 + x^2 = 400
\]
\[
x^2 = 400 - 144
\]
\[
x^2 = 256
\]
\[
x = \sqrt{256}
\]
\[
x = 16
\]
So, the length of the other leg is:
\[
\boxed{16}
\]
---
Final Answer:
\[
\boxed{5, 12, 24, 15, 16}
\]
Parent Tip: Review the logic above to help your child master the concept of pythagorean theorem perimeter worksheet.
