top button
Flag Notify
    Connect to us
      Site Registration

Site Registration

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

+1 vote
1,690 views

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

Share this puzzle
Facebook Share Button Twitter Share Button LinkedIn Share Button

7 Answers

+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

answer 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.............

answer 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

answer 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

answer 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

answer Jun 21, 2017 by anonymous
0 votes

a=square side
b=triangle side
4a=3b
Triangle area=1/2(b.b.cos30)=16√3
we find b=8
4a=3b
4a=3x8=24
a=6
Square area=a.a=6x6=36

answer Jul 29, 2018 by Halil Akansel
–2 votes

The area of square would be 32.

answer Sep 17, 2014 by Ankit Bajpai



Similar Puzzles
–1 vote

In the image, PQU is an equilateral triangle, QRVU is a square and RSTU is a rhombus. Find the perimeter of whole image?
enter image description here

+1 vote

A triangle, a square, a pentagon, a hexagon, an octagon and a circle all have an equal perimeter, which one has the smallest area?

enter image description here

0 votes

The square ABCD has a side length of 1, and AEF is an equilateral triangle. What is the area of AEF?

enter image description here

0 votes

Figure is made from a square, an equilateral triangle, and three semicircles. One semicircle has an area of 3 as shown -
enter image description here

What is the area of the lune?

0 votes

ABCD is a square and point P inside the square is such that PCD is an equilateral triangle. Find the angle α

enter image description here

...