Question

If the base of a square building and an equilateral triangle building have the same perimeter, how do the areas of their floors compare?

Answer 1

let, perimeter of square = 4a

where a = side of square

let, perimeter of the equilateral triangle = 3b

where b= side of triangle

therfore, 4a=3b

a/b = 3/4

area of the square =
`a^(2)`

are of the triangle =
`(√(3) )/(4) b^(2)`

dividing both the areas we get,

`(a^(2) )/((√(3) )/(4)b^(2) )`

`a^(2)*(4)/(√(3) b^(2))`

`(a^(2) )/(b^(2) ) * (4)/(√(3) )`

`(3^(2) )/(4^(2) ) * (4)/(√(3) )`

`(3√(3) )/(4)`

hope you understand

Explanation: