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lisov135 [29]
3 years ago
11

1. Which set of numbers

Mathematics
1 answer:
alexdok [17]3 years ago
7 0

Answer:

(5, 12, 13) are the set of numbers that could represent the length of a right triangle.

Step-by-step explanation:

In any right angle triangle sum of square of the largest side is equal to the sum of square of the other two sides.

Using pythagoras:

(Hypotenuse)^{2} = Base^{2} + Altitude^{2}

where largest side is the hypotenuse.

Case 1:  (10)^{2} \neq (5)^{2} + (5)^{2}

∵ 100 ≠ 50

Case 2:  (6)^{2} \neq (4)^{2} + (5)^{2}

36 ≠ 16 + 25

36 ≠ 41

Case 3: (13)^{2} = (5)^{2} + (12)^{2}

169 = 25 + 144

169 = 169

Since (Hypotenuse)^{2} = Base^{2} + Altitude^{2} = 169, ∴ option C is the correct answer. So, (5, 12, 13) are the set of numbers that could represent the length of a right triangle.

Case 4:  (10)^{2} \neq (7)^{2} + (8)^{2}

100 ≠ 49 + 64

100 ≠ 103

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