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Find the area of the square if square and an equilateral triangle have same perimeter?

+1 vote
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Square and Triangle

A square and an equilateral triangle have the same perimeter. If the area of the triangle is 16√3 , what is the area of the square?

posted Sep 17, 2014 by Dilbagh

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6 Solutions

+4 votes

Let the side of Equilateral triangle be t
And of square be s
By first condition
4*s = 3*t
Area of equilateral triangle = √3/4 * (side^2) = √3/4 * (t^2)
16√3/4 = √3/4 * (t^2)
So t^2 = 16*4
t = 8
Now
4*s = 3*8
s = 6
So area of square = side^2 = 6^2 = 36

solution Feb 3, 2015 by Jaspalsingh Parmar
+2 votes

Let x as side of triangle, y as side of square.
hence 3x = 4y
area of triangle = 1/2 bh, b = x , h = √3 x /2
hence √3x^2 / 4 = 16√3
x = 8
3x = 24 = 4y
y = 6
area of square = y^2 = 36.............

solution Sep 19, 2014 by Kumar Udhaya
+2 votes

let side of the triangle be b
then area of the triangle is 0.5*b*0.5*b*sqrt(3)
given area of the triangle is 16*sqrt(3)
from the above two b=8
therefore side of the square is 6 and area 36

solution Jul 5, 2015 by Kewal Panesar
0 votes

Suppose you have perimeter as 12x then each side of triangle would be 3x and for square it would be 4x.

now (√3/4)*(4x)^2 = 16√3
or (4x)^2 = 64 = 8^2
or x = 2

area of the square is (3x)^2 or 36

solution Sep 17, 2014 by Salil Agrawal
if we  have perimeter as 12x then each side of triangle would be 4x and for square it would be 3x.
Thanks  for pointing corrected :) my answer.
The two perimeters must be equal, saying that 4x = 3x is wrong (except if x is zero). How do you get x=2 ?
0 votes

Let the side of the equilateral be s, then area of the equilateral ▲= (√3s²)/4 = 16√3 => s² = 64 → s = 8

Perimeter of the equilateral ▲= 3s = 24

Perimeter of the square = 4a = 24, hence a= 6.

Area of the square a² = 6² = 36

solution Jun 21 by anonymous
–2 votes

The area of square would be 32.

solution Sep 17, 2014 by Ankit Bajpai



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