Respuesta :
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.
