Let's solve each problem step by step using the
Pythagorean Theorem, which states:
> For a right triangle:
> $$
> a^2 + b^2 = c^2
> $$
> where $a$ and $b$ are the legs, and $c$ is the hypotenuse (the side opposite the right angle).
---
1. Find the hypotenuse of a triangle with a base of 11 cm and height of 8 cm.
We are given:
- Base ($a$) = 11 cm
- Height ($b$) = 8 cm
- Hypotenuse ($c$) = ?
Use the formula:
$$
c^2 = a^2 + b^2 = 11^2 + 8^2 = 121 + 64 = 185
$$
$$
c = \sqrt{185} \approx 13.6 \text{ cm}
$$
✔ Answer: Approximately
13.6 cm
---
2. Tommy the Turtle wanders off in the zoo...
We're told:
- Mr. Gorilla walks 17 feet east.
- Then he walks 9 feet north.
This forms a right triangle where:
- One leg = 17 ft (east)
- Other leg = 9 ft (north)
- Hypotenuse = distance from start to end
So:
$$
d^2 = 17^2 + 9^2 = 289 + 81 = 370
$$
$$
d = \sqrt{370} \approx 19.2 \text{ feet}
$$
✔ Answer: Approximately
19.2 feet from his starting point.
---
3. Tom is asked to repair a roof...
Given:
- Ladder is 10 feet long (hypotenuse)
- Bottom of ladder is 6 feet from the wall (one leg)
- Need to find how high up the wall it reaches (other leg)
Let $h$ be the height:
$$
h^2 + 6^2 = 10^2
$$
$$
h^2 + 36 = 100
$$
$$
h^2 = 64
\Rightarrow h = \sqrt{64} = 8 \text{ feet}
$$
✔ Answer: The ladder reaches
8 feet up the wall.
---
4. Maria walked 3 km west and 4 km south...
She walks:
- 3 km west
- 4 km south
These form perpendicular legs of a right triangle. Distance from start is the hypotenuse.
$$
d^2 = 3^2 + 4^2 = 9 + 16 = 25
\Rightarrow d = \sqrt{25} = 5 \text{ km}
$$
✔ Answer: She is
5 km from her starting point.
---
5. Lena’s guest house is 10 m long and 12 m wide...
We need the diagonal of the rectangle, which is the hypotenuse of a right triangle with legs 10 m and 12 m.
$$
d^2 = 10^2 + 12^2 = 100 + 144 = 244
\Rightarrow d = \sqrt{244} \approx 15.62 \text{ meters}
$$
✔ Answer: Diagonal is approximately
15.62 meters
---
6. David leaves his house to go to school...
He walks:
- 200 m west
- 125 m north
Distance from home is the hypotenuse:
$$
d^2 = 200^2 + 125^2 = 40,000 + 15,625 = 55,625
\Rightarrow d = \sqrt{55,625} = 235.85 \text{ m} \quad (\text{approx})
$$
But let's check:
Is $235.85^2 = 55,625$?
Actually, $235^2 = 55,225$, $236^2 = 55,696$. So closer to 235.85.
Wait — let's compute more accurately:
$$
\sqrt{55,625} = 235.85 \text{ m} \quad \text{(correct)}
$$
Alternatively, note that:
$$
\sqrt{55,625} = \sqrt{25 \times 2,225} = 5\sqrt{2,225}
$$
But no perfect square here, so decimal is fine.
✔ Answer: Approximately
235.85 meters from starting point.
---
7. Laptop screen size...
Screen has:
- Width = 10 inches
- Height = 8 inches
Diagonal is the hypotenuse:
$$
d^2 = 10^2 + 8^2 = 100 + 64 = 164
\Rightarrow d = \sqrt{164} \approx 12.8 \text{ inches}
$$
✔ Answer: The screen size is approximately
12.8 inches.
---
✔ Final Answers Summary:
1.
13.6 cm
2.
19.2 feet
3.
8 feet
4.
5 km
5.
15.62 m
6.
235.85 m
7.
12.8 inches
Let me know if you'd like these rounded differently or explained further!
Parent Tip: Review the logic above to help your child master the concept of pythagorean theorem word problems worksheet.
