How to Increase the Sides to Double the Area of a SquareDate: 01/28/2005 at 12:16:10 From: colby Subject: double the area of a square I am puzzled as to how you would double the area of a square. Do you multiply the sides by a decimal? I can't find the right number to multiply by, or the right solution. Date: 01/30/2005 at 12:45:30 From: Doctor Wilko Subject: Re: double the area of a square Hi Colby, Thanks for writing to Dr. Math! Let's take an example. Say you have a 2ft by 2ft square. The area is 4 sq. ft. ------- | | |4 ft^2 | 2 ft (2 ft)^2 = 4 sq ft | | ------- 2 ft Now say you want to double the area of this square to 8 sq. ft. Your question is what do we have to multiply 2 by (on the original square) to be able to double the area (in this example, from 4 ft^2 to 8 ft^2)? ------- ---------- | | | | |4 ft^2 | 2 ft ===> | 8 ft^2 | (2*x) ft | | (double area) | | ------- | | 2 ft ---------- (2*x) ft 2^2 = 4 (2 * x)^2 = 8 (2 * x) = sqrt(8) 2 * x = 2 * sqrt(2) x = sqrt(2) So it looks like in this example, you'd multiply 2 by sqrt(2), then square that to double the area. Let's check it and see. (2 ft)^2 = 4 sq ft (Area of original square) If we multiply a side of length 2 by sqrt(2) and then square that, do we get 8 sq ft? (2 * sqrt(2))^2 =? 8 sq ft (2 * sqrt(2)) * (2 * sqrt(2)) =? 8 sq ft (2 * 2) * (sqrt(2) * sqrt(2)) =? 8 sq ft | | | | 4 * 2 = 8 sq ft (It checks!) So, in general, to double the area of ANY square with a side of length s, multiply s by sqrt(2), then square that, i.e. [s * sqrt(2)]^2. ---------- --------------- | | | | | s^2 sq ft| s ft ===> | | s*sqrt(2) ft | | (double area) | 2*(s^2) sq ft | ---------- | | s ft | | --------------- s*sqrt(2) ft Does this help? Please write back if you need anything else or are confused about this. - Doctor Wilko, The Math Forum http://mathforum.org/dr.math/ |
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