Pythagorean Theorem Word Problems Worksheet - Fill and Sign ... - Free Printable

Problem Set Analysis and Solutions

The worksheet provided contains several geometry-related problems. Below, I will solve each problem step by step with clear explanations.

---

#### Problem 1:
Find the hypotenuse of a triangle with a base of 11 cm and height of 9 cm.

- Solution:
The triangle described is a right triangle, where the base and height are the two legs. To find the hypotenuse, we use the Pythagorean theorem:
\[
c = \sqrt{a^2 + b^2}
\]
Here, \( a = 11 \) cm (base) and \( b = 9 \) cm (height). Substituting these values:
\[
c = \sqrt{11^2 + 9^2} = \sqrt{121 + 81} = \sqrt{202}
\]
Therefore, the hypotenuse is:
\[
\boxed{\sqrt{202}} \text{ cm}
\]

---

#### Problem 2:
Tommy the Turtle wanders off in the zoo. Mr. Gorilla sees him walk to the "1" on Clancy Road and make a right. He then walks 1.2 miles from Tommy's pen. Gilbert Giraffe saw Tommy pricing outside the giraffe area. The giraffe area is 1.6 miles from the "1" on Clancy Road. How far did Tommy walk?

- Solution:
This problem involves finding the distance Tommy walked using the Pythagorean theorem. The distances form a right triangle:
- One leg is the distance Tommy walked along Clancy Road: 1 mile.
- The other leg is the distance from the "1" on Clancy Road to the giraffe area: 1.6 miles.
- The hypotenuse represents the total distance Tommy walked.

Using the Pythagorean theorem:
\[
\text{Total distance} = \sqrt{(1)^2 + (1.6)^2} = \sqrt{1 + 2.56} = \sqrt{3.56}
\]
Therefore, the total distance Tommy walked is:
\[
\boxed{\sqrt{3.56}} \text{ miles}
\]

---

#### Problem 3:
Tom is afraid of heights above it. He is asked to reach a side of a high dock. The bottom of a ladder must be placed 6 feet from dock is slack. The ladder is 10 feet long. How far above the ground does the ladder touch the dock?

- Solution:
This problem involves a right triangle where:
- The ladder acts as the hypotenuse: 10 feet.
- The distance from the bottom of the ladder to the dock is one leg: 6 feet.
- The height above the ground where the ladder touches the dock is the other leg, which we need to find.

Using the Pythagorean theorem:
\[
\text{Height} = \sqrt{\text{Hypotenuse}^2 - \text{Base}^2} = \sqrt{10^2 - 6^2} = \sqrt{100 - 36} = \sqrt{64} = 8
\]
Therefore, the ladder touches the dock at a height of:
\[
\boxed{8} \text{ feet}
\]

---

#### Problem 4:
Sara walked 3 km west and 4 km south. Calculate how far she is from her starting point.

- Solution:
Sara's path forms a right triangle, where:
- The distance walked west is one leg: 3 km.
- The distance walked south is the other leg: 4 km.
- The straight-line distance from her starting point is the hypotenuse.

Using the Pythagorean theorem:
\[
\text{Distance} = \sqrt{(3)^2 + (4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5
\]
Therefore, Sara is:
\[
\boxed{5} \text{ km}
\]
from her starting point.

---

#### Problem 5:
Lena’s guest house is 15 m long and 12 m wide. How long is the diagonal of the house?

- Solution:
The diagonal of the guest house forms the hypotenuse of a right triangle, where:
- The length is one leg: 15 m.
- The width is the other leg: 12 m.

Using the Pythagorean theorem:
\[
\text{Diagonal} = \sqrt{(15)^2 + (12)^2} = \sqrt{225 + 144} = \sqrt{369}
\]
Therefore, the diagonal of the house is:
\[
\boxed{\sqrt{369}} \text{ m}
\]

---

#### Problem 6:
Clare learns the house to go to school. He walks 200 m west and 125 m north. Calculate how far he is from the starting point.

- Solution:
Clare's path forms a right triangle, where:
- The distance walked west is one leg: 200 m.
- The distance walked north is the other leg: 125 m.
- The straight-line distance from his starting point is the hypotenuse.

Using the Pythagorean theorem:
\[
\text{Distance} = \sqrt{(200)^2 + (125)^2} = \sqrt{40000 + 15625} = \sqrt{55625} = 235.85
\]
Therefore, Clare is approximately:
\[
\boxed{235.85} \text{ m}
\]
from his starting point.

---

#### Problem 7:
Laptop screen sizes are determined by the length of the diagonal portion of little screen, rounded to the nearest whole number. A laptop screen has a 10 inch width and the height measures 8 inches. Calculate the screen size.

- Solution:
The screen size is the diagonal of the rectangle formed by the width and height. Using the Pythagorean theorem:
\[
\text{Diagonal} = \sqrt{(10)^2 + (8)^2} = \sqrt{100 + 64} = \sqrt{164}
\]
The square root of 164 is approximately 12.81. Rounding to the nearest whole number:
\[
\boxed{13} \text{ inches}
\]

---

Final Answers:

1. \(\boxed{\sqrt{202}}\) cm
2. \(\boxed{\sqrt{3.56}}\) miles
3. \(\boxed{8}\) feet
4. \(\boxed{5}\) km
5. \(\boxed{\sqrt{369}}\) m
6. \(\boxed{235.85}\) m
7. \(\boxed{13}\) inches

---

Boxed Final Answer:
\[
\boxed{\sqrt{202}, \sqrt{3.56}, 8, 5, \sqrt{369}, 235.85, 13}
\]