Question : If the sides of a right-angled triangle are three consecutive integers, then the length of the smallest side is
Option 1: 3 units
Option 2: 2 units
Option 3: 4 units
Option 4: 5 units
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Correct Answer: 3 units
Solution :
Let one side of a right-angled triangle be $x$.
Shortest side = $x-1$
Longest side = $x +1$
Since the three sides form a right-angled triangle.
$(x+1)^2=(x-1)^2+x^2$
⇒ $x^2+1+2x=x^2+1-2x+x^2$
⇒ $x^2=4x$
⇒$x=4$
Thus, shortest side = $x-1=4-1=3$
Hence, the correct answer is 3 units.
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