Question

A square and a equalateral triangle have equal perimeter . if the diognals of the square is 12√2 cm then the area is​,...... by herons formula

Answer 1

Answer:

C

Step-by-step explanation:

Let a be the side of the square.

Diagonal of square = 12√2 cm.

By Pythagoras theorem,

a² + a² =  (12√2)²

2a² = 144 * 2

=> a² = 144

=> a = 12 cm.

Perimeter of Square = 4 * 12 = 48 cm.

Given Perimeter of Square = perimeter of Equilateral triangle.

Perimeter of equilateral triangle = 3 * Side = 48 cm

Side of Equilateral triangle = 48/3 = 16 cm.

Area of Equilateral triangle = √3/4 * Side² = √3/4 * (16)² = 64√3 cm².