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

Answer 1

The answer is Set 1,

this is because you can do Pythagoras' theorem and say that 10^2 + 24^2 must equal 26^2, so:

100 + 576 = 676

√676 = 26

And therefore Set 1 is a right-angled triangle because Pythagoras' theorem only works on right-angled triangles

Explanation:

I took the test and got 100%

Answer 2

Set 1

10 cm, 26 cm, 24 cm

Explanation:

Set 1

10 squared + 24 squared = 26 squared

100 + 576 = 676

676 = 676

Set 2

4 squared + 2 squared = 6 squared

16 + 4 = 36

20 = 36

not equal to

Set 3

14 squared + 13 squared = 15 squared

196 + 169 = 225

365 = 225

not equal to

Set 4

10 squared + 20 squared = 30 squared

100 + 400 = 900

500 = 900

not equal to

Therefore Set 1 only makes a right angle