The areas of two squares are in the ratio 9:16. The smaller square has sides of length 15cm. Calculate the size of the length of the larger square.
15/x = 3/4
If the areas are in the ratio 9:16 then the sides (which are the square root of the areas) are in the ratio √9:√16
3:4 = 15:20
the sides are in the ratio 3:4, so ...
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To find the length of the larger square, we'll need to use the given ratio of the areas and the known side length of the smaller square.
Let's start by finding the area of the smaller square using its side length of 15 cm. The formula to calculate the area of a square is A = s^2, where A represents the area and s represents the length of the side.
So, the area of the smaller square is A_small = 15 cm * 15 cm = 225 cm^2.
Now, we can set up a ratio using the areas of the two squares. The ratio is given as 9:16, which means that the area of the larger square is 16 times the area of the smaller square.
Mathematically, we can express this as:
A_large / A_small = 16 / 9.
Substituting the known values:
A_large / 225 cm^2 = 16 / 9.
Now, we can solve for A_large by cross-multiplying:
A_large = (225 cm^2 * 16) / 9
Simplifying this expression, we get:
A_large = 400 cm^2.
Since the area of a square is equal to the side length squared, we can find the side length of the larger square by taking the square root of the area:
s_large = sqrt(A_large)
Substituting the calculated value of A_large:
s_large = sqrt(400 cm^2)
Finally, calculating the square root, we find:
s_large = 20 cm.
Therefore, the side length of the larger square is 20 cm.