wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The sum of the three sides of a triangle is greater than the sum of its three ___.


A

interior angles

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

exterior angles

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

sides

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

medians

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D

medians



Let ABC be the triangle and D, E and F the midpoints of BC, CA and AB respectively.
Recall that the sum of two sides of a triangle is greater than twice the median bisecting the third side,
Hence in ΔABC, AD is a median
AB+AC>2AD

Similarly, we get,
BC+AC>2CF
BC+AB>2BE
On adding the above inequations, we get
(AB+AC)+(BC+AC)+(BC+AB)>(2AD+2CD+2BE)
2(AB+BC+AC)>2(AD+BE+CF)
AB+BC+AC>AD+BE+CF
Hence, we can say that the perimeter of a triangle is greater than the sum of the medians.


flag
Suggest Corrections
thumbs-up
4
similar_icon
Similar questions
View More
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Altitude of a triangle
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon