Given:
The diagonal of a square is
12√2cm The area of an equilateral triangle
(AT) is
64√3cm2⋯-(i)
Formula Used:
Perimeter of square
=4x Area of square
=x2 Diagonal of square
=√2.x Where,
x= side length of square
Perimeter of equilateral
∆=3a Area of equilateral
∆=√3a2∕4 Calculation:
Let teh length of side of square be
x And the length of side of equilateral
∆ be a
According to the question
√2⋅x=12√2 ⇒x=12 So, Perimeter of square
=4×12=48cm− (ii)
Area of square
(AS)=122=144cm2⋯ (iii)
Again according to the question
√3a2∕4=64√3 ⇒a2=256cm2 ⇒a=16cm So, Perimeter of equilateral
∆=3×16=48cm⋯-(iv)
From (ii) and (iv), we get
Perimeter of square
= Perimeter of equilateral
∆ Statemetn 1 is correct And from (i) and (iii), we get
= ⇒= ⇒4AS=3√3AT Statement 2 is also correct.
∴ Both the statements are correct.