Question

Two sides of a triangle have length 10 and 17. What is the range of the length of the 3rd side

Answer 1

Answer:

13.7477270849 to 19.7230829233.

Step-by-step explanation:

1. Using the pythagorean theorem, a²+b²=c², we try different combinations of given lengths 10 and 17.

2. If 10 and 17 are legs and 10²+17²=√389 = 19.7230829233, then c=19.7230829233.

3. If 10 is a leg and 17 is a hypotenuse,

10²+b²=17²

100+b²=289

b²=189

b=13.7477270849

4. The case of 17 is a leg and 10 is a hypotenuse is not possible because the hypotenuse is the longest side.

5. The range of the length of the 3rd side is 13.7477270849 to 19.7230829233.