In a trapezium, one diagonal divides the other in the ratio 2 ∶ 7. If the length of the larger of the two parallel sides is 42 cm, then what is the length (in cm) of the other parallel side?

This question was previously asked in
UP Police Assistant Operator Memory Based Full Test 3
View all UP Police Assistant Operator Papers >
  1. 14
  2. 13
  3. 12
  4. 10

Answer (Detailed Solution Below)

Option 3 : 12

Detailed Solution

Download Solution PDF

Given:

​In a trapezium, one diagonal divides the other in the ratio 2 ∶ 7.

The length of the larger of the two parallel sides is 42 cm.

Concept used:

When two triangles are similar, their corresponding angles are equal and their corresponding sides are proportional.

Calculation:

F4 Madhuri SSC 16.02.2023 D1

According to the question,

BD divides AC in a 2 : 7 ratio. 

So, AE/EC = 2/7

BC = 42

Since AD and BC are parallel to each other, ΔAED and ΔCEB are similar triangles.

​According to the concept,

AE/CE = AD/BC

⇒ 2/7 = AD/42

⇒ AD = (42 × 2)/7

⇒ AD = 12

∴ The length of the other parallel side is 12 cm.

∴ Option 3 is the correct answer.

Latest UP Police Assistant Operator Updates

Last updated on Jun 27, 2025

-> The UP Police Assistant Operator Merit List PDF has been released on 27th June 2025.

-> The UP Police Assistant Operator Notification was released for 1374 vacancies.

-> The finally appointed candidates will receive UP Police Assistant Operator Salary in the pay scale of Rs. 25,500 to Rs. 81,100.

More Plane Figures Questions

Get Free Access Now
Hot Links: teen patti master update teen patti sweet teen patti all game teen patti joy