Given four rods of length 1 meter, 3 meters, 5 meters, and 7

BTGmoderatorLU wrote:Source: Princeton Review

Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters, how many different triangles can be made using one rod for each side?

A. 6
B. 4
C. 3
D. 2
E. 1

The OA is E

Note that for a triangle, (1) the sum of any two sides must be greater than the third side and (2) the difference of any two sides must be less than the third side

Let's look at the following possibilities of triangles.

1. Sides: 1 meter, 3 meters, and 5 meters: Not possible since 1 + 3 = 4 < 5.
2. Sides: 1 meter, 3 meters, and 7 meters: Not possible since 1 + 3 = 4 < 7.
3. Sides: 1 meter, 5 meters, and 7 meters: Not possible since 1 + 5 = 6 < 7.
4. Sides: 3 meter, 5 meters, and 7 meters: Possible since 3 + 5 = 8 > 7.

The correct answer: E

Hope this helps!

-Jay
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BTGmoderatorLU wrote:Source: Princeton Review

Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters, how many different triangles can be made using one rod for each side?

A. 6
B. 4
C. 3
D. 2
E. 1

The OA is E

Since the sum of 2 sides of a triangle must be greater than the 3rd, the only option for the three sides is {3, 5, 7}. We cannot use the rod of length 1 meter in forming any triangles; we can verify that in any choice of three sides including the rod of length 1, there are two sides where the sum of the lengths is less than the length of the third side.

Answer: E