math 4 th grade

Question

The table shows the dimensions of 4 different rectangles. Each rectangle has an area of 36 square centimeters. 

Which rectangle has an area of 36 square centimeters and a perimeter of 26 centimeters?

Answer 1

A rectangle has 4 sides with each of the two pair of two sides that are opposite each other being equal in length. If the length of sides 1 and 3 are represented by x, and sides 2 and 4 by y, then the perimeter would be represented by the following equation:

2x + 2y = 26, whereas the formula for the area of the rectangle would be x * y = 36.

Assuming that each of the numbers are integers, (integer is another word for a whole number), then I start by seeing which numbers could x and y be, that when multiplied together equals 36.

Let's start with 6. 6 x 6 = 36, but that is eliminated, because that would be a square which was not stated, also, 2 x 6 = 12 plus another 2 x 6 = 12, which when added together equals 24, not 26. There are no integers that work with the next numbers up or down from 6, that is, either 7 or 5. The same is true for 8. The next numbers, however, 4 and 9, do work for the area as 9 x 4 = 36, and for the perimeter, as 2 x 9 = 18 and 2 x 4 = 8. 18 + 8 = 26.