Let's solve each of these word problems 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 longest side, opposite the right angle).
We’ll apply this to each problem.
---
1) Mark’s shortest distance home
Mark drives:
- 35 km North
- 42 km West
This forms a right triangle with legs 35 km and 42 km. The shortest path (straight line) is the hypotenuse.
$$
c^2 = 35^2 + 42^2 = 1225 + 1764 = 2989
$$
$$
c = \sqrt{2989} \approx 54.7 \text{ km}
$$
✔ Answer: 54.7 km
---
2) Diagonal of Mr. Richard’s orchard
Orchard dimensions:
- Length = 36 m
- Width = 18 m
Diagonal = hypotenuse of right triangle:
$$
c^2 = 36^2 + 18^2 = 1296 + 324 = 1620
$$
$$
c = \sqrt{1620} \approx 40.2 \text{ m}
$$
✔ Answer: 40.2 m
---
3) Diagonal of Joey’s sandwich
Sandwich is 4 cm long and 6 cm high → rectangle.
Diagonal:
$$
c^2 = 4^2 + 6^2 = 16 + 36 = 52
$$
$$
c = \sqrt{52} \approx 7.2 \text{ cm}
$$
✔ Answer: 7.2 cm
---
4) Distance from tip of tree to tip of shadow
Tree height = 15 m (vertical leg)
Shadow length = 8 m (horizontal leg)
The distance from the top of the tree to the tip of the shadow is the hypotenuse.
$$
c^2 = 15^2 + 8^2 = 225 + 64 = 289
$$
$$
c = \sqrt{289} = 17 \text{ m}
$$
✔ Answer: 17.0 m
---
5) Diagonal of Rachel’s rug
Rug dimensions:
- 11 m long
- 9 m wide
Diagonal:
$$
c^2 = 11^2 + 9^2 = 121 + 81 = 202
$$
$$
c = \sqrt{202} \approx 14.2 \text{ m}
$$
✔ Answer: 14.2 m
---
✔ Final Answers (rounded to 1 decimal place):
1)
54.7 km
2)
40.2 m
3)
7.2 cm
4)
17.0 m
5)
14.2 m
Let me know if you'd like the answers filled in on the worksheet format!
Parent Tip: Review the logic above to help your child master the concept of pythagorean theorem worksheet word problems.
