document.write( "Question 621037: the perimeter of a right triangle is 90 ft. the ratio of the legs is 5:12. what is the length of the longest leg of the triangle? \n" ); document.write( "

Algebra.Com's Answer #390537 by matt501823(7) $\"\"$ $\"About$

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The pythagorean Theorem is $\"a%5E2%2Bb%5E2=c%5E2\"$ . If you substitute in 5 and 12 for a and b respectively you get $\"5%5E2%2B12%5E2=25%2B144=169\"$ . $\"sqrt%28169%29=13\"$ . Thus the ratios of the sides must be 5, 12, and 13. Now we know that in order to maintain this ratio we must multiply the sides by a common factor such that the perimeter equals 90. To do this we can create the following equation:
\n" ); document.write( " $\"5x%2B12x%2B13x=90\"$ . We can further simplify this equation so it becomes $\"30x=90\"$ . Now we must divide both sides of the equation by 30, so we get $\"x=3\"$ . Now that we know that the common factor is 3 we can simply multiply the side length with a ratio of 13 by 3 and we get $\"13%2A3=39\"$ . Thus, the side lengths must be 15, 36, and 39 as $\"15%2B36%2B39=90\"$ . The longest side of the three is 39, so 39 is the answer. \n" ); document.write( "

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