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5 June, 18:03

The area of a certain square is 64. What would be the area of second square whose perimeter was half as large as that of the first?

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Answers (2)
  1. 5 June, 18:59
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    A square is a figure that has 4 equal sides. We also know that the perimeter is the sum of all the sides of a figure. In this case we have 4 sides each with a measure of x adding to 64in. From this information we can find out the measure of each side. Our equation follows:

    x+x+x+x=64

    4x=64

    x=16

    Now that we know that each side is 16in we can answer the question. Since we're being asked the dimensions of a square with dimensions half as large, then all we need to do is take half of 16in which is 8in.

    Answer: 8in each side.
  2. 5 June, 19:13
    0
    The area of any given square can be found by squaring the side length of that square. If s is a square's side length, then a = s². The perimeter of a square can be found by multiplying that side length by 4, since squares have four equal sides - mathematically, p = 4s. Notice what happens then when we cut the perimeter in half:

    p/2 = 4s/2

    We can either interpret this as only measuring half (2) of the square's sides, or as cutting the length of each side in half. Now notice what happens to that half-sized square's area when we substitute s/2 for s:

    a = (s/2) ² = s²/4

    While the perimeter is just divided by 2, the area is divided by 2², or 4. We can use this knowledge to find the area of the half-sized square in our problem:

    a = 64/4 = 16.

    So, the area of our square is 16 square units.
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