- #1

Karol

- 1,380

- 22

## Homework Statement

## Homework Equations

Area of triangle=(base x height)/2

## The Attempt at a Solution

a is the side of the triangle.

Area of an equilateral triangle: ##~\displaystyle \frac{a}{2h}=\tan 30^0=\frac{\sqrt{3}}{3}##

$$\rightarrow A_t=\frac{\sqrt{3}}{4}a^2$$

Side of the rectangle: (L-3a)

Total area:

$$A=(L-3a)^2+\frac{\sqrt{3}}{4}a^2$$

$$A'=2(L-3a)(-3)+\frac{\sqrt{3}}{2}a$$

$$A'=0:~a=\frac{12L}{36+\sqrt{3}}$$

There is no other value for the A'=0