each of the equal sides of an isosceles triangle is 2 cm more than its height and the base is 12 cm .find the area of the triangle.
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Let height be x
Then side= x+2
Base=12
But x is perpendicular to base
So b= 12/2=6
By Pythagoras theorem ,
(X+2)²=x²+6²
X²+4+4x=x²+36
(Either side x² cancel)
4+4x=36
4x=32
x= 32/4=8
Height= x= 8
Area=1/2×b×h
=1/2×12×8
=48cm²
Then side= x+2
Base=12
But x is perpendicular to base
So b= 12/2=6
By Pythagoras theorem ,
(X+2)²=x²+6²
X²+4+4x=x²+36
(Either side x² cancel)
4+4x=36
4x=32
x= 32/4=8
Height= x= 8
Area=1/2×b×h
=1/2×12×8
=48cm²
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