Answer:
B. The sum of the squares of the two smaller sides is equal to the square of the third side.
Step-by-step explanation:
It can be helpful to recognize that the given side lengths, 12, 16, 20 are in the ratio 3:4:5, a recognizable Pythagorean triple. That is, you may know already that the triangle is a right triangle and the sum of squares of the short sides is equal to the square of the longest side (choice B).
In case you aren't aware of common Pythagorean triples, or didn't recognize these numbers, you can try the options to see which fits.
A. The sum of the two smaller sides is 12 +16 = 28. It is NOT equal to the third side, 20.
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B. The sum of the squares of the two smaller sides is 12^2 + 16^2 = 144 + 256 = 400. This IS equal to the square of the third side: 20^2 = 400.
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C. The absolute value of the difference between the squares of the two smaller sides is |256 -144| = 112. This is NOT equal to the square of the third side, 20^2 = 400.
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D. The sum of the squares of the two smaller sides is 400 (as above). It is NOT equal to the third side, 20.
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The only answer choice that fits is choice B.
