Question
Download Solution PDFLet Δ ABC ∼ Δ QPR and \(\rm \frac{area \ of \ \Delta ABC}{area \ of \ \Delta PQR}=\frac{64}{25}\) If QP = 12 cm, PR = 10 cm and AC = 15 cm, then the length of AB is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Δ ABC ∼ Δ QPR
\(\frac{area \ of \ Δ ABC}{area \ of \ Δ PQR}=\frac{64}{25}\)
Formula used:
In similar triangles, the ratio of the areas is equal to the square of the ratio of the corresponding sides.
\(\frac{area \ of \ Δ ABC}{area \ of \ Δ PQR} = (\frac{corresponding \ side \ of \ Δ ABC}{corresponding \ side \ of \ Δ PQR})^2\)
Calculation:
\(\frac{64}{25} = (\frac{AB}{QP})^2\)
⇒ \(\frac{64}{25} = (\frac{AB}{12})^2\)
⇒ \(\frac{64}{25} = \frac{AB^2}{144}\)
⇒ \(\frac{64}{25} × 144 = AB^2\)
⇒ \(\frac{64 × 144}{25} = AB^2\)
⇒ \(\frac{9216}{25} = AB^2\)
⇒ 368.64 = \(AB^2\)
⇒ AB = \(\sqrt{368.64}\)
⇒ AB = 19.2 cm
∴ The correct answer is option (4).
Last updated on Apr 24, 2025
-> The AAI Junior Assistant Response Sheet 2025 has been out on the official portal for the written examination.
-> AAI has released 168 vacancies for Western Region. Candidates had applied online from 25th February to 24th March 2025.
-> A total number of 152 Vacancies have been announced for the post of Junior Assistant (Fire Service) for Northern Region.
-> Eligible candidates can apply from 4th February 2025 to 5th March 2025.
-> Candidates who have completed 10th with Diploma or 12th Standard are eligible for this post.
-> The selection process includes a Computer Based Test, Document Verification, Medical Examination (Physical Measurement Test), Driving Test and a Physical Endurance Test.
-> Prepare for the exam with AAI Junior Assistant Previous year papers.