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CBSE Class 10 Answered

The hypotenuse of a right triangle is 3 root 10 cm. If the smaller leg is tripled and the longer leg doubled , new hypotenuse will be 9 root 5 cm.how long are the legs of the triangle? (I need an answer in quadratic equation)
Asked by angeliquerowina | 29 May, 2018, 01:30: PM
answered-by-expert Expert Answer
begin mathsize 16px style case space 1
hypotenuse equals 3 square root of 10
let space smaller space leg space is space straight x
so space other space leg space equals square root of left parenthesis 3 square root of 10 right parenthesis squared minus straight x squared end root equals square root of 90 minus straight x squared end root
case space 2
hypotenuse equals 9 square root of 5
smaller space leg space is space 3 straight x
so space other space leg space equals square root of left parenthesis 9 square root of 5 right parenthesis squared minus 9 straight x squared end root equals square root of 405 minus 9 straight x squared end root
long space leg space is space doubled
2 square root of 90 minus straight x squared end root equals square root of 405 minus 9 straight x squared end root
square
4 open parentheses 90 minus straight x squared close parentheses equals open parentheses 405 minus 9 straight x squared close parentheses
360 minus 4 straight x squared equals 405 minus 9 straight x squared
5 straight x squared equals 45
straight x squared equals 9
straight x equals 3...... side space can apostrophe straight t space be space negative end style
Answered by Arun | 29 May, 2018, 05:45: PM
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