Question

the perimeter of an equilateral triangle us equal to perimeter of square the diagonal to the square is 9√2cm . find the area of equilateral triangle.

Answer 1

Diagonal=9√2cm

$sides \: of \: square \: are \: equal \: and \: forming \: right \: angle \: triangle \: when \: diagonal \: form \\ so \\ here \: we \: let \: side \: be \: x \\ and \: apply \: pythagoros \: theoram \\ \\ \: {x}^{2} + {x}^{2} = {(9 \sqrt{2} )}^{2} \\ 2 {x}^{2} = 162 \\ {x}^{2} = 81 \\ x = \sqrt{81} \\ x = 9 \\ \\ side \: of \: sqare \: is \: 9cm$
$perimeter \: of \: triangle \: = perimetr \: of \: square \\ \\ 3y = 4x..y \: is \: side \: of \: triangle \\ \\ 3y = 36 \\ y = 12$
$now \: area \: of \: equilateral \: triangle \\ \frac{ \sqrt{3} }{4} {y}^{2} \\ \frac{ \sqrt{3} }{4} {12}^{2} \\ \sqrt{3} \: \: 36$
Area of triangle will be 36√3