Question
Download Solution PDFIf x2 - 1, 2x and x2 + 1 are the three sides of a right angled triangle, then which of the following can be its hypotenuse?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Three sides of the right-angled triangle: x2 - 1, 2x, x2 + 1
Formula used:
In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Calculations:
Hypotenuse2 = Side12 + Side22
Let x2 + 1 be the hypotenuse.
⇒ (x2 + 1)2 = (x2 - 1)2 + (2x)2
⇒ (x2 + 1)2 = x4 - 2x2 + 1 + 4x2
⇒ x4 + 2x2 + 1 = x4 + 2x2 + 1
⇒ Since LHS = RHS
⇒ So, Hypotenuse2 = Side12 + Side22
⇒ Hence, (x2 + 1) is the hypotenuse of the given triangle.
∴ The correct answer is x2 + 1
Last updated on Jul 15, 2025
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