document.write( "Question 649397: A leg of a right triangle is 1 cm longer than its shorter leg. If the hypotenuse is 9 cm longer than the shorter leg, what are the measures of the three sides? With complete solution. \n" ); document.write( "
Algebra.Com's Answer #406966 by shweta(56)\"\" \"About 
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Let the shorter leg of a right angled triangle be 'x', hypotenuse be 'h'and other leg be 'y'
\n" ); document.write( "Given: y= x+1
\n" ); document.write( " h= x+9
\n" ); document.write( "According to the hypotenuse theorem,
\n" ); document.write( "h^2= x^2+y^2
\n" ); document.write( "(x+9)^2= x^2+(x+1)^2
\n" ); document.write( "Apply formula:(a+b)^2= a^2+b^2+2a*b
\n" ); document.write( "x^2+9^2+2*x*9= x^2+x^2+1^2+2*x*1
\n" ); document.write( "x^2+81+18x= 2x^2+1+2x
\n" ); document.write( "x^2-2x^2+18x-2x+81-1=0
\n" ); document.write( "-x^2+16x+80= 0
\n" ); document.write( "x^2-16x-80= 0
\n" ); document.write( "We get quadratic equation and need to factorise it
\n" ); document.write( "Factors Of 80= 2,2,2,2,5
\n" ); document.write( "We have to arrange the factors to get the middle term, i.e. 16
\n" ); document.write( "20= 2*2*5 and 4=2*2
\n" ); document.write( "x^2-20x+4x-80= 0
\n" ); document.write( "x(x-20)+4(x-20)= 0
\n" ); document.write( "Take (x-20) common
\n" ); document.write( "(x-20)(x+4)=0
\n" ); document.write( "x=20,-4
\n" ); document.write( "the leg of the triangle cannot be negative so the answer is 20
\n" ); document.write( "The shorter leg is 20 cm
\n" ); document.write( "Other leg,y=x+1
\n" ); document.write( " y=20+1=21cm
\n" ); document.write( "Hypotenuse,h=x+9
\n" ); document.write( " h=20+9=29cm\r
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