Question

Given that a rectangle has a length of 5/2x + 10 with a width of 5/2x + 5, which expression represents the area of the rectangle?

A. 25x^2/2 + 75x/2 + 50

B. 25x^2/4 + 75x/4 + 50

C. 25x^2/4+ 75x/2+ 50

D. 25x^2/2 + 75x/4 + 50

Answer 1

Answer:

Option C.  25x^2/4+ 75x/2+ 50

Step-by-step explanation:

A rectangle is a figure consisting of 4 sides in total with 2 pairs of equal size, defined by a length and a width. The Rectanlge Area is defined as:

$A_{R}=wl$    Eqn. (1)

where:

$A_{R}$ is the Area of Rectangle

$w$ is the width

$l$ is the length.

Now in the given question we know the following:

$w=\frac{5}{2}x+5$

$l=\frac{5}{2}x+10$

By subsitution of the above in Eqn (1) we obtain:

$A_{R} = (\frac{5}{2}x+5)(\frac{5}{2}x+10)$

(factoring out brackets we get:)

$A_{R} = \frac{25}{4}x^{2}+\frac{25}{2}x+\frac{50}{2}x+50$

(gathering all same terms we get:)

$A_{R} = \frac{25}{4}x^{2}+\frac{75}{2}x+50$

Which is the final result for $A_{R}$ and by comparing with the given options in the Question, we conclude that the expression that represents the area of the rectangle is Option C.