Question

a square and an equilateral triangle have equal perimeters.if the diagonal of square is 12 root 2 find the area of triangle

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Answer 1

Answer:

Step-by-step explanation:

Diagonal of a square = side (root 2)

12 (root 2) = side (root 2)

Side = 12cm

P of square = 12 x 4 = 48

P of triangle = 3 x a = 48

                   => a = 16

A of equilateral triangle = (root 3)/4 (a^2)

                                     = (root 3) 64

                                     = 64

Answer 2

Given:-

A square and an equilateral triangle has same Perimeter.

Dioganal of the square =

$\sqrt[24]{2} </p><p>$

To Find:-

The area of the Triangle.

Solution :-

We are given with a Square and an equilateral triangle both has same perimeter.

We need to find the area of the equilateral Triangle. But, the Only clue is that their Perimeters are same.

Let us start from the concept of Square.

We know that the sides of the square are equal and the diagonal and the two sides form a rigjt angled Triangle

By, Pythagoras Theorem.

$\begin{gathered}{a}^{2} + {a}^{2} = {( \sqrt[24]{2}) }^{2} \\ \\ {2a}^{2 } = 576 \times 2 \\ \\ {a}^{2} = 576 \\ \\ a = \sqrt{576} = 24cm\end{gathered}$

★Perimeter of the square = Perimeter of the Equilateral Triangle

Area of Equilateral Triangle =

$4*24 = 3* side \: of \: Triangle</p><p>$

Side of triangle = 4*24/3

★ Side of Triangle = 32cm

$\frac{ \sqrt{3} }{4} \times 32 \times 32 = \bold{ \red{★Area = 256 \sqrt{3} {cm}^{2} }{} }{} </p><p>$