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If the length of a rectangle is given by the expression 2 153 and the width is given by 4 68 , which radical expression represents the perimeter of the rectangle? A) 6 34 B) 14 17 C) 28 17 D) 32 17

Respuesta :

sqdancefan

Answer:

  C)  28√17

Step-by-step explanation:

The perimeter is twice the sum of the two given side lengths, so is ...

  P = 2(L +W) = 2(2√153 +4√68)

  = 2(6√17 +8√17) = 2(14√17)

  P = 28√17 . . . . . matches choice C

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This is about simplifying radicals. The applicable rules are ...

  √(ab) = (√a)(√b)

  √(a²) = |a|

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  153 = 9×17, so √153 = (√9)(√17) = 3√17

  68 = 4×17, so √68 = (√4)(√17) = 2√17

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Comment on the problem presentation

It would help if there were actually radicals in the radical expressions. We had to guess based on the spacing and the answer choices.

In any event, this problem can be worked with a calculator. Find the perimeter (≈115.45) and see which answer matches that. (That's what I did in order to verify my understanding of what the radical expressions were.)

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