Question

7) A right triangle has hypotenuse of length p cm and one side of length q cm. if p-q=1cm, find the length of third side of the triangle.​

Answer 1

Answer:

AB=√2p-1=√2q+1

Step-by-step explanation:

let hypotenuse AC= p cm

one side BC = q cm

p-q=1 given

q=p-1-------------(1)

As per Pythagoras theorem the 3rd side

AB=√AC²-BC²

=√(p²-q²)

=√( p²-(p-1)²

=√(p²-(p²-2p+1)

=√p²-p²+2p-1

=√2p-1=√2(q+1)-1

=√2q+1

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So the third side

AB=√2p-1=√2q+1