Answer:
c. 3 ft by 4 ft by 5 ft
Explanation:
You want to know which sets of measurements can form a triangle.
Triangle inequality
The triangle inequality requires ...
a + b > c
for any assignment of a, b, c to side lengths. If 'a' and 'b' are the two shortest sides, satisfying this inequality will also satisfy any other arrangement.
Choices
- a. 3 + 4 > 9 . . . . false
- b. 5 + 5 > 10 . . . . false
- c. 3 + 4 > 5 . . . . TRUE
- d. 9 + 11 > 20 . . . . false
Only the side lengths 3 ft, 4 ft, 5 ft will form a triangle.
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Additional comment
As we said the other arrangements of the triangle inequality are also satisfied for these numbers:
4 + 5 > 3
3 + 5 > 4
The garden with side lengths 3, 4, 5 will have the shape of a right triangle.