Which of the following cannot form a right-angle triangle? A triangle with side lengths of:
Select one:
a. 11 cm, 60 cm, and 61 cm.
b. 18 m, 24 m, and 30 m.
c. 37 mm, 35 mm, and 12 mm.
d. 77 m, 34 m, and 111 m.
The side lengths of a right-angle triangle follow the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Calculating the squares of the side lengths:
a. Hypotenuse^2 = 61^2 = 3721. Other two sides^2 = 11^2 + 60^2 = 121 + 3600 = 3721. Therefore, this can form a right-angle triangle.
b. Hypotenuse^2 = 30^2 = 900. Other two sides^2 = 18^2 + 24^2 = 324 + 576 = 900. Therefore, this can form a right-angle triangle.
c. Hypotenuse^2 = 37^2 = 1369. Other two sides^2 = 35^2 + 12^2 = 1225 + 144 = 1369. Therefore, this can form a right-angle triangle.
d. Hypotenuse^2 = 111^2 = 12321. Other two sides^2 = 77^2 + 34^2 = 5929 + 1156 = 7085. Therefore, this cannot form a right-angle triangle.
Therefore, the correct answer is:
d. 77 m, 34 m, and 111 m.