the hypotenuse of a right angled triangle is 1 unit greater than 2 times the base. 3rd side is 7 unit greater than base. find the sides of triangle by forming a quadratic equation?
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Step-by-step explanation:
Let, the base is X
the hypotenuse is h
the third side is p
hence, h= 2x +1
and p= x +7
using pythagoras theorem,
h^2=p^2 + x^2
=> (2x+1)^2 = ( x+7) ^2 + x^2
=> 4x^2 + 4x + 1 = x^2 + 14x + 49 +x^2
=> 2x^2-10x- 48=0
=> x^2 -5x - 24=0
=> (x-8)(x+3)=0
Hence x= 8 or x= -3 impossible
h= 2×8+1
=16+1
=17
p= 8+7
=15.
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