Let's solve each of these
Pythagoras' Theorem word problems step by step.
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🔷 Problem 1: Ladder Against a House
Given:
- The ladder is placed
5 ft away from the house (horizontal leg).
- It reaches
12 ft up the wall (vertical leg).
- We need to find the
length of the ladder, which is the
hypotenuse of the right triangle.
Using Pythagoras’ Theorem:
> $ a^2 + b^2 = c^2 $
Where:
- $ a = 5 $ ft
- $ b = 12 $ ft
- $ c = ? $ (ladder length)
$$
c^2 = 5^2 + 12^2 = 25 + 144 = 169
$$
$$
c = \sqrt{169} = 13
$$
✔ Answer: The ladder is
13 feet long.
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🔷 Problem 2: Diagonal Fence in a Rectangular Garden
Given:
- Rectangle dimensions:
12 m × 20 m
- The fence runs diagonally from one corner to the opposite corner → this is the
diagonal.
- Use Pythagoras’ Theorem to find diagonal.
Let:
- $ a = 12 $ m
- $ b = 20 $ m
- $ c = ? $ (diagonal)
$$
c^2 = 12^2 + 20^2 = 144 + 400 = 544
$$
$$
c = \sqrt{544} \approx 23.3238...
$$
Rounded to
1 decimal place:
$$
c \approx 23.3 \text{ m}
$$
✔ Answer: The fence needs to be
23.3 meters long.
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🔷 Problem 3: Sally’s Walk – Distance as the Crow Flies
Given:
- Sally walks
4 miles north, then
3 miles east.
- This forms a right triangle with legs of 4 and 3 miles.
- We want the straight-line distance (hypotenuse) from start to end point.
Use Pythagoras:
$$
c^2 = 4^2 + 3^2 = 16 + 9 = 25
$$
$$
c = \sqrt{25} = 5
$$
✔ Answer: She has walked
5 miles as the crow flies.
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✔ Final Answers:
1)
13 feet
2)
23.3 meters
3)
5 miles
All solved using
Pythagoras’ Theorem: $ a^2 + b^2 = c^2 $.
Parent Tip: Review the logic above to help your child master the concept of pythagorean theorem math problems.
