SOLUTION: how would you solve the following word problem The diagonal of a square measures 10 inches. What is the length of the sides. I know this problem uses a^2 + b^2 = c^2 and so

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Question 151984: how would you solve the following word problem
The diagonal of a square measures 10 inches. What is the length of the sides.
I know this problem uses a^2 + b^2 = c^2 and so far I have c^2=10^2 = 100. Whats next?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Ok so far: c%5E2+=+100 and c is the diagonal of the square.
The sides of the square are equal, so when you write: c%5E2+=+a%5E2%2Bb%5E2 the a and b are equal, so you can write:
c%5E2+=+a%5E2%2Ba%5E2 or
c%5E2+=+2a%5E2 Substitute c%5E2+=+100
100+=+2a%5E2 Divide both sides by 2.
50+=+a%5E2 Take the square root of both sides.
sqrt%2850%29+=+a
a+=+sqrt%2825%2A2%29
a+=+sqrt%285%5E2%2A2%29
a+=+5%2Asqrt%282%29
The length of the sides of the square are each exactly 5sqrt%282%29inches or approximately 7.1 inches.