Question

A square and am equilateral triangle have equal perimeter If the diagnol of the square is 12√2 then what is the area. Of equilateral triangle

Answer 1

Answer:

Diagonal of a square = 12$\sqrt{2}$

so the formula would be

$Diagonal^{2} = Side^{2} + Side^{2}$

$2 Side^{2} = Diagonal^{2}$

2 Side^{2} = 12$\sqrt{2}$^{2}

2 Side^{2} = 288

Side^{2}  = 144

Side = 12 units

So the perimeter of the square = 4 x Side

Perimeter of the square = 4 x 12 = 48 units

Perimeter of the equilateral triangle will also be 48 units

As it is a equilateral triangle, all the sides will be same, so the perimeter of the equilateral triangle would be S + S + S = 3S

3 x Sides of the triangle = 48 units

Side of the triangle = 16 units

So, the area of the equilateral triangle would be $\sqrt{3} / 4 Side^{2}$

Area of the equilateral triangle = $(\sqrt{3} / 4 ) * 16^{2}$

Area of the equilateral triangle = 110.848 square units

Step-by-step explanation: