Question

Which of the following represents the area of a rectangle whose length is x + 1 and whose width is x + 11?

A.) x2+ 11
B.) x2+ 12x + 11
C.) x2+ 11x + 12
D.) x2+ 10x + 11

Answer 1

The formula for area of a rectangle is A = bh or A = lw.

The length and width of this rectangle are given as follows:

l = x + 1

w = x + 11

To find the area, multiply these two together.

(x + 1)(x + 11)

Use FOIL to simplify this binomial. FOIL:

First: Refers to each first term in parentheses (x and x, in this case)

Outer: Refers to the outermost terms in each parentheses (x and 11 here)

Inner: Refers to the innermost terms in each parentheses (1 and x, in this case)

Last: Refers to the last terms in each parentheses (1 and 11 here).

Let's simplify.

(x + 1)(x + 11)

x² + 11x + 1x + 11

x² + 12x + 11

Answer:

B) x² + 12x + 11

Answer 2

Area is length * Width.

So the area of this rectangle would be

(x+1)(x+11)

This is a binomial so we can FOIL the two equations to get our answer

First

Outer

Inner

Last

For the F we multiply the first two terms in each expression together

(x+1)(x+11) x * x= x^2

For the O we multiply the two outer terms together

(x+1)(x+11) x*11= 11x

So far we have x^2 + 11x

For the I, we multiply the two inner terms together

(x+1)(x+11) 1*x= 1x or x

now we have x^2 + 11x +x

For the L, we multiply the last terms of both monomials together.

(x+1)(x+11) 1 * 11= 11

The area is x^2 +11x +x + 11

B. x^2 + 12x + 11 is your answer