If the semiperimeter of a right angled triangle be s cm and hypotenuse br x cm, then the area of triangle is
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Excellent question.
Let the perpendicular and base of traingle be l and b respectively.Then,
perimeter=l+b+x
or,
semiperimeter=l+b+x/2=s
or,l+b+x=2s
or,l+b=2s-x. (1)
also,l²+b²=x² (by Pythagoras theorem)
or, (l+b)²-2lb=x²
or, (2s-x)²-2lb=x². (from (1) )
or, (2s-x)²-x²=2lb
or, 4s²+x²-4sx-x²=2lb
or, (4s²-4sx)/2=lb
or, (2s²-2sx)=lb. (2)
Area of traingle=1/2 x lb
=1/2 x(2s²-2sx). from(2)
=s²-sx=s(s-x)
Ans
Hope it helps
Let the perpendicular and base of traingle be l and b respectively.Then,
perimeter=l+b+x
or,
semiperimeter=l+b+x/2=s
or,l+b+x=2s
or,l+b=2s-x. (1)
also,l²+b²=x² (by Pythagoras theorem)
or, (l+b)²-2lb=x²
or, (2s-x)²-2lb=x². (from (1) )
or, (2s-x)²-x²=2lb
or, 4s²+x²-4sx-x²=2lb
or, (4s²-4sx)/2=lb
or, (2s²-2sx)=lb. (2)
Area of traingle=1/2 x lb
=1/2 x(2s²-2sx). from(2)
=s²-sx=s(s-x)
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Hope it helps
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