Question

The length of 2 sides of a triangle are given. Describe the lengths possible for the third side.
22. 8ft, 12ft
23. 5in, 16in
24. 6cm, 6cm
25. 18m, 23m
26. 4yd, 7yd
27. 20km, 35km

Show work/explain how you got your answer in order to get a medal for your patronage

Answer 1

@mathstudent55 @Hero @ganeshie8 @goformit100 @mathslover @agent0smith @Mertsj @tkhunny

Answer 2

Not a good question.
Are they Right Triangles?
Do "3rd side" and "last leg" describe the same thing?

Answer 3

@tkhunny the length of 2 sides of a triangle are given. Describe the lengths possible for the third side.

Answer 4

Use your Triangle Inequality and track it down.

3 ft and 5 ft and x ft

3 + 5 > x ==> x < 8
3 + x > 5 ==> x > 2
5 + x > 3 ==> x > -2 <= Well, that doesn't help much.

One of yours, please! Let's see it.

Answer 5

I think you did it right, but I did the Pythagorean Theorem

Answer 6

This is why I asked about RIGHT triangles. That is not the question. You will find that your RIGHT TRIANGLE solution is in the range I provided, however, you must decide which side has the greatest length.

3, 5, and x? 3^2 + 5^2 = x^2 ==> \(x = \sqrt{34} = 5.8309518948453\)
3, something, and 5? Well, x = 4.

These two results are well within my general result of 2 < x < 8.

Answer 7

how does x = 4 when the sqrt of 34 is 5.8

Answer 8

?? Those are two difference cases. The first is where the missing side is the greatest and the second is where the missing side is not the greatest.