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# Geometry homework help?

Topic: Album homework help
July 18, 2019 / By Abaigael

## Best Answers: Geometry homework help?

Spencer | 6 days ago
First, you know that the figure is at least a rhombus, because all four sides are the same length (x). But we can't use the Pythagorean Theorem unless we have right triangles, and we don't have right triangles unless the figure is a square. But you can't assume that it's a square just because it looks like one on the diagram (although the other answers so far appear to have done that), so here's how you know fore sure that it's a square: In any rhombus, the diagonals bisect the angles that the corners make, and since half of a corner angle is labeled as 45 degrees, that means the corner and the opposing corner are each 90 degree angles, which means that the other two corners must also be 90 degree angles. So, we have a square, and the two triangles into which the square is separated by the diagonal are both right triangles. We are given that the hypotenuse is 6 sqrt(2) in length, and that the legs are each x. So, using the Pythagorean Theorem: a^2 + b^2 = c^2 We know that a = x and b = x, and c = 6 sqrt(2). We get the following equation, and solve for x: x^2 + x^2 = (6 sqrt(2))^2 2x^2 = 36 * 2 2x^2 = 72 x^2 = 36 x = sqrt(36) x = 6 So, the length of each side of the square is 6.
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