Calculate Rectangle Area with Dimensions (x+5) and (y+2)

Video Solution

Solution Steps

00:00 Find the expression for the rectangle's area

00:03 We'll use the formula for calculating rectangle area (side times side)

00:07 We'll substitute appropriate values according to the given data and solve to find the area

00:14 We'll properly open parentheses and multiply X by the 2 factors:

00:23 Now we'll multiply 5 by the 2 factors

00:36 And this is the solution to the question

Step-by-Step Solution

Let's begin by reminding ourselves of the formula to calculate the area of a rectangle: width X length

$S=w⋅h$

Where:

S = area

w = width

h = height

We extract the data from the sides of the rectangle in the figure.

$w=x+5$ $h=y+2$

We then substitute the above data into the formula in order to calculate the area of the rectangle:

$S=w⋅h=(x+5)(y+2)$

We use the formula of the extended distributive property:

$(a+b)(c+d)=ac+ad+bc+bd$

We once again substitute and solve the problem as follows:

$S=(x+5)(y+2)=(x)(y)+(x)(2)+(5)(y)+(5)(2)$

$(x)(y)+(x)(2)+(5)(y)+(5)(2)=xy+2x+5y+10$

Therefore, the correct answer is option C: xy+2x+5y+10.