Question

HELP WITH THIS PROBLEM PLEASE!!

Answer 1

Answer : Perimeter = 24√6 cm and

Area = 96√3 cm²

Solution :
_________

Given that : The height of equilateral triangle = 12√2 cm.

As we know that : All side of equilateral triangle are equals.

Let, the side of equilateral triangle = 2x cm.

Then, By Pythagoras theoram :

${(2x)}^{2} = {(x)}^{2} + {(height)}^{2} \\ \\ = > 4 {x}^{2} = {x}^{2} + {(12 \sqrt{2} )}^{2} \\ \\ = > 3 {x}^{2} = 288 \\ \\ = > {x}^{2} = 96 \\ \\ = > x = 4 \sqrt{6} cm$

So, the side of equilateral triangle = 2x = 2×4√6 = 8√6 cm.

Now, Perimeter of equilateral triangle :

$3 \times 8 \sqrt{6} = 24 \sqrt{6} \: cm$

and Area of equilateral triangle

$\frac{ \sqrt{3} }{4} \times {(8 \sqrt{6}) }^{2} \\ \\ = > \frac{ \sqrt{3} }{4} \times 384 \\ \\ = > 96 \sqrt{3} \: {cm}^{2}$