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Two sides of a triangle are 5 centimeters and 6 centimeters. What is the range of possible lengths for the third side? Explain your reasoning using complete sentences.

Sagot :

sqdancefan

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Answer:

  1 < third side < 11

Step-by-step explanation:

If you join the given sides at one end and lay the 5 cm side on top of the 6 cm side, you find the other ends are separated by a distance of 6-5 = 1 cm. In order for the triangle to have non-zero area, the third side must be longer than 1 cm.

If you lay the given sides end-to-end along a line, the far ends are separated by a distance of 6+5 = 11 cm. In order for the triangle to have non-zero area, the third side must be shorter than 11 cm.

The range of possible lengths of the third side is from 1 cm to 11 cm, not including those end values.

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This is a consequence of the triangle inequality, which requires the sum of any two sides of a triangle exceed the length of the third side.

the range of possible lenths is 1 cm-11 cm

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