Question

Given that a rectangle has a length of 5 2 x + 10 with a width of 5 2 x + 5, which expression represents the area of the rectangle? A) 25x2 2 + 75x 2 + 50 B) 25x2 4 + 75x 4 + 50 C) 25x2 4 + 75x 2 + 50 D) 25x2 2 + 75x 4 + 50

Answer 1

Answer:

C

Step-by-step explanation:

Apply FOIL method (First, Outer, Inner, Last) to multiply the length and width binomial expressions.

Answer 2

Answer:

Option c is correct

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

Step-by-step explanation:

Area of the rectangle (A) is given by:

$A= lw$               ....[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 $\frac{5}{2}x+10$ with a width of $\frac{5}{2}x+5$

⇒l = $\frac{5}{2}x+10$

and w =  $\frac{5}{2}x+5$

Substitute in [1] we have;

$A = (\frac{5}{2}x+10) \cdot (\frac{5}{2}x+5)$

⇒$A = \frac{25}{4}x^2+\frac{25}{2}x+\frac{50}{2}x+50$

Combine like terms we have;

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

therefore, the expression represents the area of the rectangle is,  $\frac{25}{4}x^2+\frac{75}{2}x+50$