suppose height of a right angled triangle is 1 less than two times its base. It's hypotenuse is 7 less than 3 times its base. Find all the sides of the right angled triangle.
answers are:base=6
height=15
hypotenuse=17
please explain this answer.
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Let,
height=2b-1
hyp.=3b-7
base=b
::b^2+b^2=hyp.^2
( by Pythagorus theorem)
(2b-1)^2+^2=(3b-7)^2
=4b^2+1-4b+b^2=9b^2-42b+49
=9b^2-42b+49=5b^2-4b+1
::we get ,
=4b^2-38b+48=0
::divide all terms by 2,we get
2b^2-19b+24=0
2^2-16-3+24
2(-8)-3(-8)=0
::base=8
{height=2(8)-1=16-1=15}
{hyp.=3(8)-7=24-7=17}
_______Abhinav Vilas Giri
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