Grades 5-6 Video Solutions 2015-Level 5&6 Video Solutions 2015 problem16

Video Transcription

Question number 16. The area of a rectangle is 12. The lengths of its sides are natural numbers. The perimeter of this rectangle could be which one of the following five numbers?  We are calculating the area of the rectangle. And so let's write down the formula. The formula  would be area here is equal to length times width. We know that the answer is 12. We know that the products here are only of natural numbers. So we can quickly run through the  possibilities of all the dimensions. We can have product of 1 and 12, a product of 2 and 6, and finally a product of 3 and 4. And if we were to switch the roles of length and width,  we would have these numbers transposed, but essentially we're talking about the same three  rectangles. And now let's look at the perimeter. The formula for that is perimeter is twice the  length plus twice the width. And so we can compute it in each of the cases with dimensions of 1 and  12. The perimeter here would be 26, which is a choice. With 2 and 6, the perimeter would be 16,  which is not a choice. And with 3 and 4, the perimeter would be 14, which is also not a choice.  So of all the possible numbers listed, only one matches our calculations. And so the answer here is that 26 could be a perimeter of such a rectangle. So the answer is B, 26.

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