In an obtuse-angled triangle ABC, the length of its longest side AB is 50 cm and one of the other two sides is 42 cm. If the area of the triangle is 294 cm2 , what is the length (in cm) of its third side?

This question was previously asked in
SSC CHSL Exam 2024 Tier-I Official Paper (Held On: 11 Jul, 2024 Shift 4)
View all SSC CHSL Papers >
  1. 15√(21)
  2. 2√(58)
  3. 12√(43)
  4. 8√(35)

Answer (Detailed Solution Below)

Option 2 : 2√(58)
Free
SSC CHSL General Intelligence Sectional Test 1
1.6 Lakh Users
25 Questions 50 Marks 18 Mins

Detailed Solution

Download Solution PDF

Given:

In an obtuse-angled triangle ABC,

Length of the longest side AB = 50 cm

One of the other two sides = 42 cm

Area of the triangle = 294 cm2

Formula used:

Area of a triangle = (1/2) × base × height

Using Heron's formula for the area of a triangle:

Area = √(s(s-a)(s-b)(s-c))

where s = (a+b+c)/2 is the semi-perimeter.

Calculation:

Let the third side be c cm.

Given area = 294 cm2

Using the area formula:

294 = (1/2) × 50 × h

⇒ h = (294 × 2)/50 = 588/50 = 11.76 cm

Now, using Heron's formula:

Semi-perimeter s = (50 + 42 + c)/2

Area = √((92+c)/2 ((92+c)/2 - 50) ((92+c)/2 - 42) ((92+c)/2 - c)) = 294

Let's simplify this step-by-step:

294 = √((92+c)/2 ((92+c)/2 - 50) ((92+c)/2 - 42) ((92+c)/2 - c))

Squaring both sides:

2942 = (92+c)/2 ((92+c)/2 - 50) ((92+c)/2 - 42) ((92+c)/2 - c)

Simplify to find c.

On solving, we find:

The length of the third side is 2√(58) cm.

Latest SSC CHSL Updates

Last updated on Jul 9, 2025

-> The Staff selection commission has released the SSC CHSL Notification 2025 on its official website on 23rd June 2025.

-> The SSC CHSL Apply Online 2025 has been started and candidates can apply online on or before 18th July.

-> The SSC has released the SSC CHSL exam calendar for various exams including CHSL 2025 Recruitment. As per the calendar, SSC CHSL Application process will be active from 23rd June 2025 to 18th July 2025. 

-> The SSC CHSL is conducted to recruit candidates for various posts such as Postal Assistant, Lower Divisional Clerks, Court Clerk, Sorting Assistants, Data Entry Operators, etc. under the Central Government. 

-> The SSC CHSL Selection Process consists of a Computer Based Exam (Tier I & Tier II).

-> To enhance your preparation for the exam, practice important questions from SSC CHSL Previous Year Papers. Also, attempt SSC CHSL Mock Test.  

-> The UGC NET Exam Analysis 2025 for the exam conducted on June 25 is out.

-> Bihar Police Admit Card 2025 has been released at csbc.bihar.gov.in.

More Mensuration Questions

Get Free Access Now
Hot Links: teen patti yes teen patti bonus teen patti 500 bonus