SOLUTION: A square had a diagnol of 10cm. How long are each of the legs?
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Question 419547: A square had a diagnol of 10cm. How long are each of the legs?
Answer by algebrahouse.com(1659) (Show Source): You can put this solution on YOUR website!
"A square had a diagonal of 10cm. How long are each of the legs?"
Make a right triangle, with each leg being x, and the diagonal being 10.
Then, substitute them into the pythagorean theorem.
a^2 + b^2 = c^2 {Pythagorean Theorem....a and b are legs, c is the hypotenuse}
x^2 + x^2 = 10^2 {substituted into pythagorean theorem}
2x^2 = 100 {combined like terms and squared 10}
x^2 = 50 {divided both sides by 2}
x = √50 {took square root of both sides}
x = √25 √2 {broke down square root of 50}
x = 5√2 {evaluated square root of 25 to be 5}
5√2 would be the measure of each leg (in simplest radical form)
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