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

ABC is an equilateral triangle of side 4a. Length of its altitude is .

A
23a
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
79a
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
43a
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 23a


Given: Length of each side of the equilateral triangle = 4a
Construction: Draw a perpendicular from A to BC. Let this meeting point be D.

In ABD and ACD,
AB = AC
( All sides of an equilateral triangle are equal)
AD = AD (Common)
ADB=ADC=90
ABDACD
(By RHS congruency)

BD = DC = 2a (by cpct)

In ABD,
AB2=AD2+BD2 (By pythagoras theorm)
AD2=AB2BD2
AD2=(4a)2(2a)2
AD2=16a24a2
AD2=12a2
AD=23a
Altitude of an equilateral triangle with side 4a will be 23a.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Criteria for Congruency
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon