Question
Download Solution PDFFind the length of one side of a rhombus whose area is 24 cm2 and the sum of the lengths of its diagonals is 14 cm.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Area of the rhombus = 24 cm2
Sum of the lengths of its diagonals = 14 cm
Concept used:
The diagonals of a rhombus always bisect each other at an angle of 90°.
Area of a rhombus =
(a + b)2 = (a - b)2 + 4ab
Calculation:
Let, the length of the diagonals of the rhombus be P and Q respectively. (Where P > Q)
According to the concept,
PQ/2 = 24
⇒ PQ = 48
According to the question,
P + Q = 14 ---(1)
⇒ (P + Q)2 = 196
⇒ (P - Q)2 + 4PQ = 196
⇒ (P - Q)2 = 196 - 4PQ
Putting the value of PQ in the equation,
⇒ (P - Q)2 = 196 - 4 × 48
⇒ (P - Q)2 = 196 - 192
⇒ (P - Q)2 = 4
⇒ (P - Q) = ± 2
⇒ (P - Q) = 2 [∵ P > Q, taking +2] ---(2)
Adding equation (1) and (2), we get,
P + Q + P - Q = 14 + 2
⇒ 2P = 16
⇒ P = 8 cm
So, Q = 8 - 2 = 6 cm
According to the concept,
ΔCOD is a right-angled triangle at O.
So, DO = OB = 8/2 = 4 cm
AO = OC = 6/2 = 3 cm
Now, DC =
∴ The length of each side of the rhombus is 5 cm.
Last updated on Jul 22, 2025
-> The Railway Recruitment Board has scheduled the RRB ALP Computer-based exam for 15th July 2025. Candidates can check out the Exam schedule PDF in the article.
-> RRB has also postponed the examination of the RRB ALP CBAT Exam of Ranchi (Venue Code 33998 – iCube Digital Zone, Ranchi) due to some technical issues.
-> SSC Selection Post Phase 13 Admit Card 2025 has been released @ssc.gov.in
-> TS TET Result 2025 has been released @tgtet.aptonline.in.
-> TNPSC Group 4 Answer Key 2025 has been released at tnpsc.gov.in
-> There are total number of 45449 Applications received for RRB Ranchi against CEN No. 01/2024 (ALP).
-> The Railway Recruitment Board (RRB) has released the official RRB ALP Notification 2025 to fill 9,970 Assistant Loco Pilot posts.
-> The official RRB ALP Recruitment 2025 provides an overview of the vacancy, exam date, selection process, eligibility criteria and many more.
->The candidates must have passed 10th with ITI or Diploma to be eligible for this post.
->The RRB Assistant Loco Pilot selection process comprises CBT I, CBT II, Computer Based Aptitude Test (CBAT), Document Verification, and Medical Examination.
-> This year, lakhs of aspiring candidates will take part in the recruitment process for this opportunity in Indian Railways.
-> Serious aspirants should prepare for the exam with RRB ALP Previous Year Papers.
-> Attempt RRB ALP GK & Reasoning Free Mock Tests and RRB ALP Current Affairs Free Mock Tests here
-> Bihar Police Driver Vacancy 2025 has been released @csbc.bihar.gov.in.
->UGC NET Final Asnwer Key 2025 June has been released by NTA on its official site