Question

a square and equilateral triangle has equal perimeter. If the diagonal of the square is 12√2 then find the area​

Answer 1

Step-by-step explanation:

let a be the side of square

by Pythagoras theorem

(a^2) + (a^2) = 12^2 *2

2a^2 = 144*2

a^2 = 144

a= 12 units

let l be the length of equilateral triangle

perimeter of triangle=3*l=perimeter of sq

(given)

perimeter of triangle=4*12=48 = 3*l

hence l = 16 units

area of equilateral triangle =( (√3)/4)*l^2

=( (√3) /4)*16 = 16√3 unit square

area of square = 12^2 = 144 unit square