Question

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

A
173.2cm2;11.32
B
173.2cm2;19.32
C
173.2cm2;17.32
D
173.2cm2;14.32

Solution

## The correct option is B $$173.2 cm^{2}; 17.32$$Given, perimeter of equilateral triangle is $$60 cm$$.Perimeter of equilateral triangle$$= 60 cm$$3$$\times$$ side $$= 60$$$$\therefore$$ side $$= \dfrac { 60 }{ 3 } = 20 cm$$.Area of equilateral triangle $$=\dfrac { \sqrt { 3 } { (side) }^{ 2 } }{ 4 } \\ =\dfrac { \sqrt { 3 } \times { 20 }^{ 2 } }{ 4 } \\ =\quad 100\sqrt { 3 } \quad { cm }^{ 2 }\quad =\quad 173{ .2\quad cm }^{ 2 }\quad$$Height of equilateral triangle $$=\dfrac { \sqrt { 3 } { (side) } }{ 2 } \\ =\dfrac { \sqrt { 3 } \times { 20 } }{ 2 } \\ =\quad 10\sqrt { 3 } \quad { cm }\quad =\quad 17.3{ 2\quad cm }\quad$$Mathematics

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