Question

Which of these four sets of side lengths will form a right triangle?

Set 1
10 cm, 26 cm, 24 cm

Set 2
4 in., 2 in., 6 in.

Set 3
14 mm, 13 mm, 15 mm

Set 4
10 ft, 30 ft, 20 ft

Set 1
Set 2
Set 3
Set 4

Answer 1

Set 1 Yes

Set 2 No

Set 3 and Set 4 ???

Explanation:

Use the converse of the Pythagorean theorem. Square the lengths and see if 2 results add up to the third result.

So, Set 1

`10^(2) = 100 \\26^(2) = 676\\24^(2) = 576` 100 + 576 = 676 Therefore we have a right triangle

Set 2

`4^(2) = 16\\2^(2) = 4\\6^(2) = 36`

16 + 4 ≠ 36 Therefore we do NOT have a right triangle

I will let you do Set 3 and Set 4. OK?

Answer 2

set 1 is the answer ............................................................