Sean is trying to find the area of a square, • The side length of the square is equivalent to the side length of an equilateral triangle,
The perimeter of the equilateral triangle is 24x + 18.
Find the expression that models the area of the square

An equilateral Triangle has 3 equal sides.

Divide the perimeter by 3 to get the length of one side.

24x + 18 / 3 = 8x + 6

The area of a square is S^2

Area = (8x+6)^2

Apply the perfect square formula to get:

64x^2 + 96x + 36

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.