Question
Download Solution PDFIn ∆ ABC, D and E are points on sides AB and AC, such that DE ΙΙ BC. If AD = x + 3, DB = 2x − 3, AE = x + 1 and EC = 2x − 2, then the value of x is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
AD = x + 3, DB = 2x − 3, AE = x + 1 and EC = 2x − 2
Concept used:
When two triangles are similar, their corresponding angles are equal and their corresponding sides are proportional.
Calculation:
As DE ΙΙ BC, and ∠A is common in both triangle ABC and triangle ADE
So, ABC ∼ ADE
So,
AB/AD = AC/AE
⇒ (x + 3 + 2x - 3)/(x + 3) = (x + 1 + 2x - 2)/(x + 1)
⇒ (3x)/(x + 3) = (3x - 1)/(x + 1)
⇒ 3x2 + 3x = 3x2 - x + 9x - 3
⇒ 3x = 8x - 3
⇒ 5x = 3
⇒ x = 3/5
∴ The value of x is \({{3} \over 5}\).
Last updated on Jun 13, 2025
-> The SSC CGL Notification 2025 has been released on 9th June 2025 on the official website at ssc.gov.in.
-> The SSC CGL exam registration process is now open and will continue till 4th July 2025, so candidates must fill out the SSC CGL Application Form 2025 before the deadline.
-> This year, the Staff Selection Commission (SSC) has announced approximately 14,582 vacancies for various Group B and C posts across government departments.
-> The SSC CGL Tier 1 exam is scheduled to take place from 13th to 30th August 2025.
-> Aspirants should visit ssc.gov.in 2025 regularly for updates and ensure timely submission of the CGL exam form.
-> Candidates can refer to the CGL syllabus for a better understanding of the exam structure and pattern.
-> The CGL Eligibility is a bachelor’s degree in any discipline.
-> Candidates selected through the SSC CGL exam will receive an attractive salary. Learn more about the SSC CGL Salary Structure.
-> Attempt SSC CGL Free English Mock Test and SSC CGL Current Affairs Mock Test.
-> Candidates should also use the SSC CGL previous year papers for a good revision.