Question

The length and width of a rectangle are shown below.50 - X2x+10

Answer 1

The area of a rectangle is length times width.

We simply mutliply and distribute the expressions for length and width.

Given,

Length

`2x+10`

Width

`50-x`

Thus, the area is:

`A=(2x+10)(50-x)`

We use the distributive property [(a+b)(c+d) = ac + ad + bc + bd] to multiply this expression out:

`\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}`

From the answer choices, the correct answer is:

C