Answer:
Option c is correct
[tex]\frac{25}{4}x^2+\frac{75}{2}x+50[/tex]
Step-by-step explanation:
Area of the rectangle (A) is given by:
[tex]A= lw[/tex] ....[1]
where,
l is the length and w is the width of the rectangle.
As per the statement:
Given that a rectangle has a length of [tex]\frac{5}{2}x+10[/tex] with a width of [tex]\frac{5}{2}x+5[/tex]
⇒l = [tex]\frac{5}{2}x+10[/tex]
and w = [tex]\frac{5}{2}x+5[/tex]
Substitute in [1] we have;
[tex]A = (\frac{5}{2}x+10) \cdot (\frac{5}{2}x+5)[/tex]
⇒[tex]A = \frac{25}{4}x^2+\frac{25}{2}x+\frac{50}{2}x+50[/tex]
Combine like terms we have;
[tex]A = \frac{25}{4}x^2+\frac{75}{2}x+50[/tex]
therefore, the expression represents the area of the rectangle is, [tex]\frac{25}{4}x^2+\frac{75}{2}x+50[/tex]
Answer:
C
Step-by-step explanation:
Apply FOIL method (First, Outer, Inner, Last) to multiply the length and width binomial expressions.
