Respuesta :
s = 3x - 15 is the required expression for perimeter of table top
Perimeter of square tabletop is 240 cm
Solution:
A square tabletop has an area given as:
[tex](9x^2 - 90x+225) cm^2[/tex]
The dimensions of the tabletop have the form cx - di ,where cand d are whole numbers
To find perimeter of tabletop when x = 25 centimeters
Let us first find the length of each side of square
Given area is:
[tex]area = (9x^2 - 90x+225)[/tex]
We know that,
[tex]area = (side)^2 = s^2[/tex]
Therefore,
[tex]s^2 = (9x^2 - 90x+225)\\\\s^2 = (3x - 15)(3x - 15)\\\\s^2 = (3x - 15)^2[/tex]
Taking square root on both sides,
s = 3x - 15
The above expression is the required expression for perimeter of table top
To find perimeter when x = 25 centimeter
The perimeter of square is given as:
[tex]perimeter = 4s[/tex]
perimeter = 4(3x - 15)
Substitute x = 25
perimeter = 4(3(25) - 15)
perimeter = 4(60) = 240
Therefore perimeter of square tabletop is 240 cm
