SOLUTION: The perimeter of a rectangle is 26 units. Each of the length and width of the rectangle is Measured in natural numbers. What is the largest area in square units that the rectangle

Question 227002: The perimeter of a rectangle is 26 units. Each of the length and width of the rectangle is Measured in natural numbers. What is the largest area in square units that the rectangle could have?

Found 2 solutions by lilmama50, jsmallt9:
Answer by lilmama50(7) (Show Source): You can put this solution on YOUR website!
The largest area possible for this rectangle is .

Take the perimeter of the rectangle 26 units and divide by 4, the number of sides the rectangle has. Which gives you 6.5 units... since the numbers are natural numbers round the number off to use it as the value of one of the sides. In this case that would be 7. To find the value of the other two sides, just multiply 7 by 2 (since the rectangle has two pairs of equal sides) which gives you 14, subtract this value(14) from the total perimeter which gives you 12. Divide that new value (12) by 2 to give you the value of the other two sides. The other value is 6.

Now take the width value multiply it by the length value to receive the area value in squared units. Thus giving you 42 units squared.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
The perimeter of any polygon is the sum of the lengths of all the sides. In a rectangle there are two equal sides we call the length and two other equal sides we call the width. So the perimeter is the sum of the two equal lengths and the two equal widths.

Perhaps the easiest way to solve your problem is to realize that the sum of one length and one width would be half of the the perimeter. So in your problem length + width = 13 (which is half of the total perimeter of 26).

You are also told that the length and width are natural numbers (1, 2, 3, ...). So we want two natural numbers that add up to 13. They are 1 and 12, 2 and 11, 3 and 10, 4 and 9, 5 and 8, and 6 and 7.

We are asked to find the largest area any of these pairs can make. Since area of a rectangle is length times width, A = l*w, we have to multiply each of these pairs to see which area is the largest. 1*12 = 12, 2*11 = 22, etc. I'll leave the rest for you.
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