Question
the area of the outer square is
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GPT 3.5
equal to the area of the inner square plus the area of the four triangles formed by the outer square and the inner square.
Let the side length of the inner square be "x" units. The area of the inner square is x^2 square units.
The side length of the outer square is 2x units. The area of the outer square is (2x)^2 = 4x^2 square units.
The area of each triangle is 1/2 * base * height. The base of each triangle is x units and the height is x units. So, the area of one triangle is 1/2 * x * x = 1/2x^2 square units. Since there are 4 triangles, the total area of all four triangles is 4 * 1/2x^2 = 2x^2 square units.
Therefore, the area of the outer square is 4x^2 = 2x^2 + x^2 = the area of the inner square + the area of the four triangles.
Let the side length of the inner square be "x" units. The area of the inner square is x^2 square units.
The side length of the outer square is 2x units. The area of the outer square is (2x)^2 = 4x^2 square units.
The area of each triangle is 1/2 * base * height. The base of each triangle is x units and the height is x units. So, the area of one triangle is 1/2 * x * x = 1/2x^2 square units. Since there are 4 triangles, the total area of all four triangles is 4 * 1/2x^2 = 2x^2 square units.
Therefore, the area of the outer square is 4x^2 = 2x^2 + x^2 = the area of the inner square + the area of the four triangles.
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