9514 1404 393
Answer:
2. G 10.72 units
3. B 3.6, 6, 4.8
Step-by-step explanation:
2. The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the sides.
14^2 = 9^2 + CB^2
196 = 81 + CB^2 . . . . find the square values
115 = CB^2 . . . . . . . . subtract 81
√115 = CB ≈ 10.72 . . . . . matches G
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3. You know that lengths 3, 4, 5 form a right triangle. This is a special triple for several reasons. One of them is that it is the smallest integer Pythagorean triple. Another is that it is the only Pythagorean triple that is an arithmetic sequence (has constant differences between lengths).
You can use this as a reference to look at the choices offered.
A. The lengths 3.2, 4.1 and 5.0 have constant differences of 0.9. The shortest length is not 3 times this value, so this is not a right triangle.
B. The lengths 3.6, 4.8, 6 have constant differences of 1.2. These numbers are 3, 4, and 5 times that difference, so these segments will form a right triangle.
C, D. The longest length is an integer. The sums of the squares of the decimal values will not be integers, so these are not right triangles.
4.5^2 +6.7^2 = 65.14 not 8^2
5.2^2 +8.5^2 = 99.29 not 10^2
