1 View

Question : What is the area of a triangle having a perimeter of 32 cm, one side of 11 cm, and the difference between the other two sides is 5 cm?

Option 1: $8\sqrt{30}$ cm2

Option 2: $5\sqrt{35}$ cm2

Option 3: $6\sqrt{30}$ cm2

Option 4: $8\sqrt{2}$ cm2


Team Careers360 24th Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

Correct Answer: $8\sqrt{30}$ cm 2


Solution : Let the sides of the triangle be $a$, $b$, and $c$.
Given Perimeter = 32 cm
⇒ $a+b+c=32$ ...... equation (1)
One side, let $a$ =11 cm
Also, the difference between the other two sides, $b−c=5$........ equation (2)
Performing equation (1) + equation (2)
$a+2b=37$
⇒ $11+2b=37$
⇒ $2b=26$
⇒ $b=13$ cm
Now, using equation (2),
$c=b−5$
⇒ $c=13−5=8$ cm
Area of the triangle according to Heron's formula = $\sqrt{s(s−a)(s−b)(s−c)}$ where $s$ is the semi-perimeter
$s=\frac{11+13+8}{2} = 16$ cm
Area $= \sqrt{16(16−11)(16−13)(16−8)}$
$= \sqrt{16(5)(3)(8)}$
$= 8\sqrt{30}$ cm 2
Hence, the correct answer is $8\sqrt{30}$ cm 2 .

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books