Question

A landscape architect drew a plan of a flower and vegetable garden with a triangular walkway

between each section. What lengths, in feet, could not be used to form the triangular walkway?

F.) 5,8,9
G.) 6,8,4
H.) 7,2,5
J.) 7,8,9

Answer 1

H.) 7,2,5

Explanation:

You want to know which set of lengths could not be used as the sides of a triangle.

Triangle inequality

The triangle inequality requires the sum of the two shorter sides of a triangle exceed the length of the longer side;

F. 5 + 8 > 9 . . . can be used

G. 4 + 6 > 8 . . . can be used

H. 2 + 5 = 7 . . . cannot be used for the walkway

J. 7 + 8 > 9 . . . can be used

The lengths 2, 5, 7 cannot be used to form a triangle.

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Additional comment

Such a "triangular walkway" (2, 5, 7) would look like a single walk, 7 feet long. The "triangle" would have no area.