Discussion

Explanation:

Let the three angles be a − d, a and a + d.
∴ (a − d) + a + (a + d) = 180
∴ a = 60.

Since (a + d) is the largest angle it will be opposite the largest side i.e., 13 and a will be opposite second largest side i.e., 12. 

The triangle along with the angles are shown below.


Applying the cosine rule, we get;
 
Cos 60 = (x2 + 132 − 122)/(2 × x × 13)
 
∴ x = 10.65, 2.34.
 
Inradius = Area/Semiperimeter.
 
When x = 10.65, the semiperimeter = (10.65 + 13 + 12)/2 = 17.825.
 
∴ Inradius = [(1/2) × 10.65 × 13 × Sin60]/17.825 = 3.36.
 
When x = 2.34, the semiperimeter = (2.34 + 13 + 12)/2 = 13.67.
 
∴ Inradius = [(1/2) × 2.34 × 13 × Sin60]/13.67 = 0.963 ≈ 1.
 
Hence option (d).

» Your doubt will be displayed only after approval.


Doubts


Feedback

Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.


© 2024 | All Rights Reserved | Apti4All