Delhi Police Constable practice question
In triangle ABC, D and E are points on AB and AC respectively such that DE is parallel to BC, and AD : DB = 1 : 4. If BC = 30 cm, find the length of DE.
From a Delhi Police Constable Quantitative Aptitude practice set · Quantitative Aptitude
Tap an option to check your answer.
Show answer and explanation
Correct answer: (C) 6 cm
Since DE || BC, triangle ADE ~ triangle ABC (AA similarity, as ∠A is common and ∠ADE = ∠ABC as corresponding angles). AD : DB = 1 : 4, so AD : AB = 1 : 5. By similarity, DE/BC = AD/AB, so DE = BC × 1/5 = 30 × 1/5 = 6 cm.
हिंदी में प्रश्न
त्रिभुज ABC में, D और E क्रमशः AB और AC पर स्थित बिंदु इस प्रकार हैं कि DE, BC के समांतर है, तथा AD : DB = 1 : 4 है। यदि BC = 30 सेमी है, तो DE की लंबाई ज्ञात कीजिए।
उत्तर जाँचने के लिए किसी विकल्प पर टैप करें।
उत्तर और व्याख्या देखें
सही उत्तर: (C) 6 सेमी
चूँकि DE || BC है, इसलिए त्रिभुज ADE ~ त्रिभुज ABC (AA समरूपता, क्योंकि ∠A उभयनिष्ठ है और संगत कोणों के रूप में ∠ADE = ∠ABC)। AD : DB = 1 : 4, अतः AD : AB = 1 : 5। समरूपता से, DE/BC = AD/AB, अतः DE = BC × 1/5 = 30 × 1/5 = 6 सेमी।
More solved Quantitative Aptitude questions
- Two positive integers x and y are such that log₁₀x + log₁₀y = 4, and x : y = 25 : 4. Find the value of x + y.
- Convert a speed of 17 m/s into km/hr.
- If 21 men working 6 hours a day can complete 1 unit(s) of work in 18 days, in how many days can 7 men working 8 hours a day complete 2…
- The average age of 15 persons increases by 2.5 years when a person aged 27 years is replaced by a new person. Find the age of the new…
- A trade bill worth Rs. 1200 is due 3 years from now. If the prevailing interest rate is 8% per annum, find the present worth of the sum…
- Two towers of equal height stand on opposite sides of a straight road that is 160 m wide. From a point on the road between the two towers…