Which of these four sets of side lengths will form a right triangle? set 1 4 cm, 5 cm, 6 cm set 2 8 in., 12 in., 20 in. set 3 10 mm, 20 mm, 30 mm set 4 12 ft, 16 ft, 20 ft set 1 set 2 set 3 set 4

D

Step-by-step explanation:

because yes

 The correct option is (D) SET 4.

Step-by-step explanation:  We are to select the correct set of side lengths that will form a right-angled triangle.

To form a right-angled triangle, we must have the following relation:

Perpendicular² + Base² = Hypotenuse².

Hypotenuse is the length of the largest side; perpendicular and base are the two legs of the triangle.

SET 1 :  14 cm, 5 cm, 6 cm.  

We have

Therefore,

Perpendicular² + Base² ≠ Hypotenuse².

So, this set will not form a right-angled triangle.

SET 2 :  8 in., 12 in., 20 in.  

We have

Therefore,

Perpendicular² + Base² ≠ Hypotenuse².

So, this set will not form a right-angled triangle.

SET 3 :  10 mm, 20 mm, 30 mm.  

We have

Therefore,

Perpendicular² + Base² ≠ Hypotenuse².

So, this set will not form a right-angled triangle.

SET 4 :  12 ft, 16 ft, 20 ft.  

We have

Therefore,

Perpendicular² + Base² = Hypotenuse².

So, this set will form a right-angled triangle.

Thus, the SET 4 will form a right-angles triangle.

Option (D) is correct.