Question

A square and an equilateral triangle have equal perimeter. if the diagonal of the square is 12root2 cm then area of triangle is

Answer 1

Given :

A square and an equilateral triangle have equal perimeter

The diagonal of the square is 12$\sqrt{2}$ cm

To Find :

The area of triangle

Solution :

According to question

Let The side of square = S  cm

Let The side of equilateral triangle = s  cm

square and an equilateral triangle have equal perimeter

∵ The perimeter of square =  4 × side

                                            = 4 × S

And

The perimeter of equilateral triangle = 3 × side

                                                             = 3 × s

∵ The diagonal of the square = 12$\sqrt{2}$ cm               ....1

∵ The diagonal of the square = side × √2             .....2

From eq1 and eq2

12$\sqrt{2}$ cm = side × √2

So, Side of square = S=  $\sqrt{2}$ cm

Since, A square and an equilateral triangle have equal perimeter

So,  4 × S = 3 × s

Or,   4 ×  $\sqrt{2}$ = 3 × s

Or,   s = $\dfrac{4\sqrt{2}}{3}$

i.e The side of equilateral triangle = s = $\dfrac{4\sqrt{2}}{3}$ cm

Since The Area of equilateral triangle = A = $\dfrac{\sqrt{3}}{4}$ × (side)²

                                                                     = $\dfrac{\sqrt{3}}{4}$ × ($\dfrac{4\sqrt{2}}{3}$ )²

                                                                     = $\dfrac{8\sqrt{3}}{9}$ cm²

Hence, The Area of equilateral triangle is $\dfrac{8\sqrt{3}}{9}$ cm²  . Answer

Answer 2

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