Question

There is an equilateral triangle of side 5 cm The maximum number of equilateral triangles (of side 1 cm) cut out will be



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Answer 1

The side of equilateral triangle is 5cm and other side is 1 cm

Area of equilateral triangle of side 5cm

$\tt\dfrac{ \sqrt{3} }{4} a {}^{2} \: = \: \dfrac{ \sqrt{3} }{4} \times (5) {}^{2} \: = \: \dfrac{ \sqrt{3} }{4} \times 25$

Area of small equilateral triangle

$\tt \dfrac{ \sqrt{3} }{4} \times (1) {}^{2} \: \: = \: \: \dfrac{ \sqrt{3} }{4}$

So number of small equilateral triangle cut in big equilateral triangle is

$\tt\ \: \: = \: \: \: \: \: \dfrac{ \frac{ \sqrt{3} }{4} \times 25}{ \frac{ \sqrt{3} }{4} } \: \: \: = \: \: 25$