Question

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

• A. 25
• B. 20
• C. 15
• D. 10

Answer 1

The correct option is A 25

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

Then area of equilateral triangle side 5 cm=$\frac{\sqrt{3}}{4}{a}^2=\frac{\sqrt{3}}{4}\times (5{)}^2=\frac{\sqrt{3}}{4}\times 25c{m}^2$

And area of small equilateral triangle side 5 cm=$\frac{\sqrt{3}}{4}{a}^2=\frac{\sqrt{3}}{4}\times (1{)}^2=\frac{\sqrt{3}}{4}\times 1c{m}^2$

So number of small equilateral triangle cut in big equilateral triangle =$\frac{\frac{\sqrt{3}}{4}\times 25}{\frac{\sqrt{3}}{4}\times 1}=25$