The area of a rectangle is length times width.
We simply mutliply and distribute the expressions for length and width.
Given,
Length
[tex]2x+10[/tex]
Width
[tex]50-x[/tex]
Thus, the area is:
[tex]A=(2x+10)(50-x)[/tex]
We use the distributive property [(a+b)(c+d) = ac + ad + bc + bd] to multiply this expression out:
[tex]\begin{gathered} A=(2x+10)(50-x) \\ A=(2x)(50)-(2x)(x)+(10)(50)-(10)(x) \\ A=100x-2x^2+500-10x \\ A=-2x^2+90x+500 \end{gathered}[/tex]
From the answer choices, the correct answer is:
C
