Answer:
Step-by-step explanation:
Given: A square tabletop has an area of [tex](9x^2-90x+225)cm^2[/tex].The dimensions of the tabletop have the form cx-d, where c and d are whole numbers.
To find: Expression for the perimeter of the tabletop and the perimeter when x=25 centimeters.
solution: Since, we know that area of square =[tex](side)^2[/tex], and we are given Area=[tex](side)^{2}[/tex]=[tex]9x^2-90x+225[/tex]
⇒[tex]s^{2}=(3x-15)(3x-15)[/tex]
⇒[tex]s^2=(3x-15)^2[/tex]
⇒[tex]s=3x-15[/tex]
Thus, side=[tex]3x-15[/tex].
Now, Perimeter of square is given as =4s
⇒[tex]4s=4(3x-15)=12x-60[/tex] which is the required expression for the perimeter.
Perimeter when x=25cm, [tex]12x-60=12(25)-60=300-60=240cm[/tex].
Therefore, Perimeter=240 cm.
