which set of numbers can represent the side lengths, in centimeters, of a right triangle?\n8, 12, 15\n10…
which set of numbers can represent the side lengths, in centimeters, of a right triangle?\n8, 12, 15\n10, 24, 26\n12, 20, 25\n15, 18, 20
Answer
Explanation:
Step1: Recall Pythagorean theorem
For a right - triangle with side lengths (a), (b), and (c) (where (c) is the hypotenuse), (a^{2}+b^{2}=c^{2}).
Step2: Check option 1 (8, 12, 15)
(8^{2}+12^{2}=64 + 144=208), and (15^{2}=225). Since (208\neq225), this is not a right - triangle.
Step3: Check option 2 (10, 24, 26)
(10^{2}+24^{2}=100 + 576 = 676), and (26^{2}=676). Since (10^{2}+24^{2}=26^{2}), this is a right - triangle.
Step4: Check option 3 (12, 20, 25)
(12^{2}+20^{2}=144+400 = 544), and (25^{2}=625). Since (544\neq625), this is not a right - triangle.
Step5: Check option 4 (15, 18, 20)
(15^{2}+18^{2}=225 + 324=549), and (20^{2}=400). Since (549\neq400), this is not a right - triangle.
Answer:
10, 24, 26