Answer :
The sets that can form a right triangle are: a. 20 inches, 21 inches, 29 inches, 20 yards, 21 yards, 29 yards, 65 cm, 72 cm, 97 cm, 3 meters, 5 meters, 4 meters.
Let’s analyze each set of side lengths to determine which ones form a right triangle:
a. 20 inches, 21 inches, 29 inches:
- These side lengths satisfy the Pythagorean theorem: [tex]20^2 + 21^2 = 29^2[/tex]
- Therefore, this set forms a right triangle.
b. 11 feet, 60 feet, 63 feet:
- These side lengths do not satisfy the Pythagorean theorem: [tex]11^2 + 60^2 \neq 63^2[/tex]
- So, this set does not form a right triangle.
c. 9 miles, 15 miles, 27 miles:
- These side lengths do not satisfy the Pythagorean theorem: [tex]9^2 + 15^2 \neq 27^2[/tex]
- Thus, this set does not form a right triangle.
d. 20 yards, 21 yards, 29 yards:
- These side lengths satisfy the Pythagorean theorem: [tex]20^2 + 21^2 = 29^2[/tex]
- Hence, this set forms a right triangle.
e. 65 cm, 72 cm, 97 cm:
- These side lengths satisfy the Pythagorean theorem: [tex]65^2 + 72^2 = 97^2[/tex]
- Therefore, this set forms a right triangle.
f. 3 meters, 5 meters, 4 meters:
- These side lengths satisfy the Pythagorean theorem: [tex]3^2 + 4^2 = 5^2[/tex]
- Thus, this set forms a right triangle.
Complete Question:
Select all side lengths that form a right triangle.
a. 20 inches, 21 inches, 29 inches
b. 11 feet, 60 feet, 63 feet
c. 9 miles, 15 miles, 27 miles
d. 20 yards, 21 yards, 29 yards
e. 65cm,72cm,97cm
f. 3 meters, 5 meters, 4 meters
Final answer:
To determine if a set of side lengths form a right triangle, we can use the Pythagorean theorem. Applying this to each set of side lengths given, we find that only the set 20 yards, 21 yards, 29 yards and the set 65 cm, 72 cm, 97 cm form right triangles.
Explanation:
To determine if a set of side lengths form a right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Applying this to each set of side lengths given:
- 20 inches, 21 inches, 29 inches: Not a right triangle because 20^2 + 21^2 ≠ 29^2
- 11 feet, 60 feet, 63 feet: Not a right triangle because 11^2 + 60^2 ≠ 63^2
- 9 miles, 15 miles, 27 miles: Not a right triangle because 9^2 + 15^2 ≠ 27^2
- 20 yards, 21 yards, 29 yards: Forms a right triangle because 20^2 + 21^2 = 29^2
- 65cm, 72cm, 97cm: Forms a right triangle because 65^2 + 72^2 = 97^2
- 3 meters, 5 meters, 4 meters: Not a right triangle because 3^2 + 5^2 ≠ 4^2
Learn more about Pythagorean theorem here:
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