Question

a square and an equilateral triangle have an equal perimeter if a diagonalis 12root 2 cm. find area of triangle​

Answer 1

a square and an equilateral triangle have an equal perimeter if a diagonalis 12root 2 cm. find area of triangle

Answer 2

Answer :

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