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Q: The area of a rectangle is 100 inches the perimeter is 40 a second rectangle has the same area but a different perimeter. Is the second rectangle a square?

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No, it is not. I'll give you two examples of a rectangle with a perimeter of 1. The first rectangle has dimensions of 1/4x1/4. The area is 1/16. The second rectangle has dimensions of 3/8x1/8. The area is 3/64. You can clearly see that these two rectangles have the same perimeter, yet the area is different.

This is possible because you add perimiters but multiply areas. Consider a 2 x 4 rectangle and a 1 x 5 rectangle. The first has a perimeter of 12 (2+2+4+4), and an area of 8 (2 x 4). The second rectangle has a perimeter of 12 also (1+1+5+5), but an area of 5 (5 x 1). The closer a rectangle is to a perfect square, the larger the area will be, because a square maximizes area. A 3 x 3 square also has a perimeter of 12, but an area of 9. Heres another way to think about it: a rectangle that is one inch tall and 100 inches wide would have a perimeter of 202 inches, and an area of 100 square inches. If you added one inch to the side so that it was 101 inches wide, you would add 2 inches to the perimeter, but only one square inch to the area. However, if you made it one inch taller, you would still add 2 inches to the perimeter, but you would DOUBLE the area to 200 square inches.

No.For example, a 1 metre * 72 metre rectangle and a 8 metre * 9 metre rectangle both have areas of 72 square metres. But the perimeter of the first is 146 metres while that of the second is 34 metres.

Yes, your statement is dimensionally correct. But your formula is incorrect, and possibly ambiguous. First, the perimeter is only a simple sum involving length and width IF the figure is a rectangle. Second, the perimeter of the rectangle is double what you have stated: P = 2L + 2W

You can`t be sure of the individual sides. A one inch by sixteen inch rectangle, an eight by two inch rectangle, a four inch by four inch rectangle all have the same area (16 square inches) but the first rectangle`s sides add up to 34, the second rectangle`s sides add up to 20, the third rectangle`s sides add up to 16

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No. In the first place, the word is "multiply", not "times", and in the second place, to get the width you divide the perimeter by two and then subtract the length (there are alternative methods, but none of them is even close to multiplying the length by the perimeter).

The question cannot be answered. First, there is no information as to which measure of the rectangle is 14 units: a diameter, the perimeter, the area. Second, the answer to the question above does not provide sufficient information to answer the question.

Since the perimeter of a rectangle is 2 * length + 2 * width, 2l + 2w = 36 And since the length is twice the width, l = 2w Thus, you substitute 2w into the l in the first equation to get, 2(2w) + 2w = 36 4w + 2w = 36 6w = 36 w = 6 Plug the value of w into the second equation, l = 2(6) This will give you a length of 12. Since the area of rectangle is l * w, we just substitute the values in for length and width, l * w = 6 * 12 = 72 And that would be in square inches of course.

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