Question

What is the area of the figure shown below, which is not drawn to scale?

A rectangle has length 5x minus 7 and width 3x minus 5.
A. 15x2+35

B. 15x2-46x+35

C. 15x2-12x+35

D. 4x3

Answer 1

To find the area of the rectangle, you multiply the length by the width.

Given:
- Length = \( 5x - 7 \)
- Width = \( 3x - 5 \)

The area \( A \) can be calculated as:

\[
A = \text{Length} \times \text{Width} = (5x - 7)(3x - 5)
\]

Now, let's expand this expression using the distributive property (often referred to as the FOIL method for binomials):

\[
A = (5x)(3x) + (5x)(-5) + (-7)(3x) + (-7)(-5)
\]

Calculating each term:

1. \( (5x)(3x) = 15x^2 \)
2. \( (5x)(-5) = -25x \)
3. \( (-7)(3x) = -21x \)
4. \( (-7)(-5) = 35 \)

Now, combining all these terms together:

\[
A = 15x^2 - 25x - 21x + 35
\]

Combine the \( x \) terms:

\[
A = 15x^2 - 46x + 35
\]

Thus, the area of the rectangle is:

\[
\boxed{15x^2 - 46x + 35}
\]

This corresponds to option B.