Question

the length and width of a rectangle are shown below.
rectangle with length 2x+10 and width 50 - x
which expression represents the area, in square units, of the rectangle?
a. $2x^2 - 90x - 500$
b. $-2x^2 - 90x - 500$
c. $-2x^2 + 90x + 500$
d. $2x^2 + 90x + 500$

Explanation:

Step1: Recall area formula

Area = length × width

Step2: Substitute values

Area = $(2x + 10)(50 - x)$

Step3: Expand the product

$(2x)(50) + (2x)(-x) + 10(50) + 10(-x) = 100x - 2x^2 + 500 - 10x$

Step4: Combine like terms

$-2x^2 + (100x - 10x) + 500 = -2x^2 + 90x + 500$

Answer:

C. $-2x^2 + 90x + 500$