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 Jun 3, 2025
-> The Staff Selection Commission has officially released the SSC Selection Post Phase 13 Notification 2025 on its official website at ssc.gov.in.
-> A total number of 2423 Vacancies have been announced for various selection posts under Government of India.
-> The Computer Based Exam is scheduled from 24th July to 4th August, 2025. Candidates will be able to apply online from 2nd June 2025 to 23rd June 2025.
-> The SSC Selection Post Phase 13 exam is conducted for recruitment to posts of Matriculation, Higher Secondary, and Graduate Levels.
-> The selection process includes a CBT and Document Verification.
-> Some of the posts offered through this exam include Laboratory Assistant, Deputy Ranger, Upper Division Clerk (UDC), and more.
-> Enhance your exam preparation with the SSC Selection Post Previous Year Papers & SSC Selection Post Mock Tests for practice & revision.