Question

Please give me the correct answer ​

Answer 1

Answer: Choice D)  7.5 inches, 18 inches, 19.5 inches

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Explanation:

The Pythagorean theorem converse can be used to determine if we have a right triangle or not.

The converse says that if a^2 + b^2 = c^2 is a true equation, then we have a right triangle.

The value of c is always the longest side. The order of 'a' and b doesn't matter (usually b is larger than or equal to 'a'). So we could have $a \le b < c$ or $b \le a < c$, but convention usually leans toward the first inequality mentioned.

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In choice A, we have the following steps

a^2 + b^2 = c^2

(7.5)^2 + (18)^2 = (21.5)^2

380.25 = 462.25

Since the third equation is false, this means the first equation is false for those a,b,c values. Choice A is not a right triangle. We can cross it off the list.

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In choice B, we have a = 7.5, b = 19.5 and c = 21.5

So,

a^2 + b^2 = c^2

(7.5)^2 + (19.5)^2 = (21.5)^2

436.5 = 462.25

which is also false. Cross choice B off the list.

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With choice C we have: a = 18, b = 19.5, c = 21.5

a^2 + b^2 = c^2

(18)^2 + (19.5)^2 = (21.5)^2

704.25 = 462.25

Cross choice C off the list since the third equation is false.

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In choice D, we have the sides a = 7.5, b = 18, c = 19.5

a^2 + b^2 = c^2

(7.5)^2 + (18)^2 = (19.5)^2

380.25 = 380.25

We get the same number on both sides, so the third equation is true. Consequently, this leads to the first equation being true for those a,b,c values. Choice D is a right triangle, and it's the final answer.

Answer 2

Answer:

D. 7.5, 18, 19.5

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