SOLUTION: the question is to find the area of a square with a diagnol length of 15radical 2

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Question 134840: the question is to find the area of a square with a diagnol length of 15radical 2
Answer by solver91311(24713) About Me  (Show Source):
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The diagonal of a square forms an isoceles right triangle with two of the sides. Using Pythagoras, and remembering that the legs of the triangle are the same length, we have c=15sqrt%282%29, and since a=b, a%5E2%2Bb%5E2=a%5E2%2Ba%5E2=2a%5E2. That means:

2a%5E2=%2815sqrt%282%29%29%5E2

2a%5E2=225%282%29

a%5E2=225

a=15

The area of a square is given by the measure of one of the sides squared, so if the side measures 15, the area is: A=15%5E2=225 square units.