Here is the step-by-step solution to each of the Pythagorean Theorem word problems, rounded to the nearest tenth as requested.
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Problem 1:
*Dan secures a ladder firmly to the wall to dust a photo frame mounted on the wall. The foot of the ladder is placed 6 feet from the wall. If the top of the ladder rests 8 feet up the wall, what is the length of the ladder?*
This forms a right triangle:
- One leg (distance from wall) = 6 ft
- Other leg (height on wall) = 8 ft
- Hypotenuse = length of ladder = ?
Using the Pythagorean Theorem:
a² + b² = c²
→ 6² + 8² = c²
→ 36 + 64 = c²
→ 100 = c²
→ c = √100 =
10.0 feet
✔ Answer: 10.0 feet
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Problem 2:
*If the playing surface of a carom board is a square of length 28 inches, what is the diagonal length of the playing surface?*
A square’s diagonal splits it into two right triangles.
- Each leg = 28 inches
- Diagonal = hypotenuse
a² + b² = c²
→ 28² + 28² = c²
→ 784 + 784 = c²
→ 1568 = c²
→ c = √1568 ≈
39.6 inches
✔ Answer: 39.6 inches
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Problem 3:
*Carlos flies his drone 5 feet above the ground. He rotates the drone to the right. So far, the drone has flown a total of 12 feet. How far is the drone from the start point?*
This describes a right triangle:
- Vertical leg (height) = 5 ft
- Horizontal leg (ground distance traveled) = 12 ft
- Distance from start point = straight-line hypotenuse
a² + b² = c²
→ 5² + 12² = c²
→ 25 + 144 = c²
→ 169 = c²
→ c = √169 =
13.0 feet
✔ Answer: 13.0 feet
*(Note: This is a classic 5-12-13 Pythagorean triple.)*
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Problem 4:
*A ship is on its maiden voyage to the mystery island. According to the map, it has to travel 99 miles to the north and then, 20 miles to the west to reach the island. Find the shortest route that leads to the mystery island.*
The shortest route is the straight-line distance (hypotenuse) from start to finish.
- North leg = 99 miles
- West leg = 20 miles
a² + b² = c²
→ 99² + 20² = c²
→ 9801 + 400 = c²
→ 10201 = c²
→ c = √10201 =
101.0 miles
✔ Answer: 101.0 miles
*(Note: 99-20-101 is also a Pythagorean triple!)*
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Problem 5:
*For her boat model, Dahlia cut a piece of fabric in the shape of a right triangle. If the length of the longest side was 8 inches and one of other two sides measured 4 inches, what was the length of the other side?*
Longest side = hypotenuse = 8 inches
One leg = 4 inches
Find the other leg.
Use Pythagorean Theorem rearranged:
a² + b² = c² → b² = c² - a²
→ b² = 8² - 4²
→ b² = 64 - 16
→ b² = 48
→ b = √48 ≈
6.9 inches
✔ Answer: 6.9 inches
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✔ Final Answers:
1.
10.0 feet
2.
39.6 inches
3.
13.0 feet
4.
101.0 miles
5.
6.9 inches
All answers are rounded to the nearest tenth as instructed.
Parent Tip: Review the logic above to help your child master the concept of pythagoras theorem worksheet grade 7.
