Question

The area of an equilateral triangle and area of square are in the ration 3:2. If the length of the
diagonal of square is 60cm. let us write by calculating perimeter of an soseeds triangle
​

Answer 1

Step-by-step explanation:

Let square has side a and triangle t

Given, 4a=3t⇒a= 43

t Diagonial of square =2

a=>2

a=12

2

⇒a=12cm⇒t=

3

4

×12=16cm

Area of equilateral triangle =

4

3

t

2

=

4

3

(256)=64

3

Answer 2

Answer: 180 cm

Step-by-step explanation:

$area of square = \frac{1}{2} \times {d}^{2} {where\: d\: is \:diagonal}$

$= \frac{1}{2} \times {60}^{2}$

$=1800$

$\frac{area \: of \: equilateral \: triangle}{area \: of \: square} = \frac{\sqrt{3} }{2} \\ \frac{area \: of \: equilateral \: triangle}{1800} = \frac{\sqrt{3} }{2} \\ area \: of \: equilateral \: triangle= \frac{\sqrt{3} }{2} \times 1800 \\ area \: of \: equilateral \: triangle = 900 \sqrt{3} \\ but \: we \: know \: area \: of \: equilateral \: triangle = \frac{\sqrt{3} }{4} \times {a}^{2} \\ or, \: \frac{\sqrt{3} }{4} \times {a}^{2} = 900 \sqrt{3} \\ or \: a = 60 \\ therefore, \: perimeter \: of \: triangle \: = 3 \times 60 \\ = 180cm$