The rectangular region shown has been divided into nine square regions, all different in size. The area of square 3 is 64 cm. The area of square 5 is 81cm. what is the area of the rectangle?
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Solicitors Regulation Authority
To find the area of the rectangle, we first need to determine the dimensions of each square region.
Let's denote the side lengths of square 3 and square 5 as "x" and "y" respectively.
We are given that the area of square 3 is 64 cm^2, so its side length is the square root of 64, which is 8 cm (since 8 * 8 = 64).
Similarly, for square 5, we are given that its area is 81 cm^2, so its side length is the square root of 81, which is 9 cm (since 9 * 9 = 81).
Now we know that square 3 has a side length of 8 cm and square 5 has a side length of 9 cm.
Looking at the picture, we can see that square 3 is twice the size of square 1, square 4 is twice the size of square 2, and square 5 is twice the size of square 3.
Using this pattern, we can determine the side lengths of squares 1 and 2. Since square 3 has a side length of 8 cm, square 1 must have a side length of 4 cm (half of 8 cm), and square 2 must have a side length of 2 cm (half of 4 cm).
Similarly, square 4 has a side length of 16 cm (twice the size of square 2), and square 6 has a side length of 18 cm (twice the size of square 3).
Now, let's find the dimensions of the rectangle. The width of the rectangle is the sum of the side lengths of squares 2, 3, 5, and 6, which is 2 cm + 8 cm + 9 cm + 18 cm = 37 cm.
The length of the rectangle is the sum of the side lengths of squares 1, 3, 4, and 5, which is 4 cm + 8 cm + 16 cm + 9 cm = 37 cm.
Therefore, the area of the rectangle is the product of its length and width, which is 37 cm * 37 cm = 1369 cm^2.