Question

what is the answer of the question - The square and an equilateral triangle have equal perimeters. If the diagonal of the square is 12 root over 2 CM, then the area of the triangle is......

Answer 1

diagonal of square is = 12 root 2

a root 2 = 12

a = 12 cm

Perimeter of Square = 12 * 4 = 48 cm

Side of triangle = 48 / 3 = 16 cm

Area = root 3 / 4 * 16 * 16

= 64 root 3

Ans : 64 root 3

Answer 2

Perimeter of square = 4*Side of square ,

Perimeter of equilateral traingle = 3* side of traingle,
let side of square = S, and traingle = T

According to data ,

4S = 3T,

Area of square = S^2 = 1/2*D^2

here D is diagonal of square,

Area of square = 144,
=> Side of square = 12

Now side of traingle = 4*12/3 = 16

area of equilateral traingle = ✓3/4* T^2

area of equilateral traingle = 64✓3

The answer is 64✓3 , What I told was right, If I am wrong at calculations then I am sorry !!