Calculate the area and the height of an equilateral triangle whose perimeter is 60 cm.

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$173.3 11.32

$173.2 19.32

$173.2 17.32

$173.2 14.32

answer is C.

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Detailed Solution

Perimeter of a triangle = sum of all sides
∴ x+x+x=60
3x=60
x=20 cm
∴ the sides of the equilateral triangle is 20cm
now , we will find the height of the triangle
I.e DC
AC2=AD2+DC2…(By pythagoras theorem)
(20)2=(10)2+DC2 400=100+DC2 DC2= 400-100
DC2= 300
DC=√300
√300= 10√3 = 10(1.732)=17.320
∴ DC =14.320 CM
therefore , the height of triangle is 17.320 Area of triangle= ½* b* h
=½*20*17.320
=10*17.320
Therefore, the area of a equilateral triangle is 173.2 sq/cm and height is 17.320.
Type- CBSE
Subject- Mathematics
Chapter-
Topic- Relation between speed, distance and time
Sub topic-

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