Question

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

Answer 1

solutions is done in above pic

Answer 2

Answer:

perimeter = 3×side

60 = 3×side

side = 60÷3 = 20

in order to find area in an absence of height

By using Heron's formula

area =\sqrt {s(s-a)(s-b)(s-c)}

note: sqrt stands for square root

since it is an equilateral triangle, therefore

a=b=c=20cm

s=(a+b+c)÷2

= (20+20+20)÷2

=60÷2 =30cm

so, area = \sqrt {30(30-20)(30-20)(30-20)}

\sqrt {30×10×10×10}

10 \sqrt {30×10}

10×10 \sqrt {3}

=100 \sqrt {3}