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

Answer:  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[tex]5^2+6^2=25+36=61,\\\\14^2=196.[/tex]Therefore,Perpendicular² + Base² ≠ Hypotenuse².So, this set will not form a right-angled triangle.SET 2 :  8 in., 12 in., 20 in.  We have[tex]8^2+12^2=64+144=208,\\\\20^2=400.[/tex]Therefore,Perpendicular² + Base² ≠ Hypotenuse².So, this set will not form a right-angled triangle.SET 3 :  10 mm, 20 mm, 30 mm.  We have[tex]10^2+20^2=100+400=500,\\\\30^2=900.[/tex]Therefore,Perpendicular² + Base² ≠ Hypotenuse².So, this set will not form a right-angled triangle.SET 4 :  12 ft, 16 ft, 20 ft.  We have[tex]12^2+16^2=144+256=400,\\\\20^2=400.[/tex]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.