The perimeter of the small square is one-third the perimeter of the large square. What are the side lengths of the squares?
small square side = x
large square side = x + 2
small square perimeter: 4(x) = 4x
large square perimeter: 4(x+2) = 4x+8
3(4x)= 4x +8
12x= 4x+8
8x=8
x=1
thank you that was very helpful
why do you multiply it by 3?
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To find the side lengths of the squares, we need to set up an equation based on the given information.
Let's first recall that the perimeter of a square is the sum of all its sides. Therefore, the perimeter of the small square is:
Perimeter of small square = 4 * side length of small square = 4 * x
Similarly, the perimeter of the large square is:
Perimeter of large square = 4 * side length of large square = 4 * (x + 2)
According to the given information, the perimeter of the small square is one-third the perimeter of the large square. Mathematically, this can be expressed as:
Perimeter of small square = (1/3) * Perimeter of large square
Substituting the above values, we have:
4 * x = (1/3) * (4 * (x + 2))
Now, let's solve this equation to find the value of x:
4 * x = (1/3) * (4 * (x + 2))
4 * x = (4/3) * (x + 2)
12 * x = 4 * (x + 2) (multiplied both sides by 3)
12 * x = 4 * x + 8 (distributed 4 to both terms)
12 * x - 4 * x = 8 (subtracted 4 * x from both sides)
8 * x = 8 (combined like terms)
x = 1 (divided both sides by 8)
Therefore, the side length of the small square (x) is 1.
To find the side length of the large square, we substitute the value of x back into the equation:
Side length of large square = x + 2 = 1 + 2 = 3.
Hence, the side lengths of the squares are:
Small square side = 1
Large square side = 3