SOLUTION: If a right triangle has a hypotenuse of the 5 radical 5 cm and one side is twice as long as the other side, what is the length of its shortest side?. (Simplified radical)

Algebra ->  Pythagorean-theorem -> SOLUTION: If a right triangle has a hypotenuse of the 5 radical 5 cm and one side is twice as long as the other side, what is the length of its shortest side?. (Simplified radical)      Log On


   

Question 1043473: If a right triangle has a hypotenuse of the 5 radical 5 cm and one side is twice as long as the other side, what is the length of its shortest side?. (Simplified radical)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the length of the shortest side = +x+
The length of the longer side is +2x+
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Use Pythagorean theorem
+%28+5%2Asqrt%285%29+%29%5E2+=+x%5E2+%2B+%282x%29%5E2+
+25%2A5+=+x%5E2+%2B+4x%5E2+
+5x%5E2+=+5%2A25+
+x%5E2+=+25+
+x+=+5+
and
+2x+=+10+
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The shortest side is 5 cm
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check:
+%28+5%2Asqrt%285%29+%29%5E2+=+x%5E2+%2B+%282x%29%5E2+
+%28+5%2Asqrt%285%29+%29%5E2+=+5%5E2+%2B+10%5E2+
+25%2A5+=+25+%2B+100+
+125+=+125+
OK