Question

It is square find the
length if perimeter 36 cm
find area of triangle​

Answer 1

$perimeter \: = 3x \: = 36 \: cm \\ x \: = 12 \: cm \\ in \: triangle \: (abd) \: applying \: \\ pythagoras \: theorem. \\ {x}^{2} = \frac{x {}^{2} }{2} + {ad}^{2} \\ {ad}^{2} = \frac{3x {}^{2} }{4} = ad = \frac{ \sqrt{3} }{2} {x} \\ height \: = \frac{ \sqrt{3} }{2} \times 12 = 6 \sqrt{3} \\ area \: = \frac{1}{2 } \times base \times height \\ = \frac{1}{2} \times x \times \frac{ \sqrt{3} }{2} {x} \\ = \frac{ \sqrt{3} }{4} {x}^{2} \: = \frac{ \sqrt{3} }{4} \times ( {12)}^{2} \\ area \: = 36 \sqrt{3} {cm}^{2}$