Donovan is painting a large wall orange. yesterday, he painted a square-shaped area that was 7x square feet. today, he extended one side of the orange area by 3 feet and the other consecutive side by 4 feet

The correct answer is D. 7x < 7x + 7√7x + 12

Complete question and statement:

Donovan is painting a large wall orange. Yesterday, he painted a square-shaped area that was 7x square feet. Today, he extended one side of the orange area by 3 feet and the other consecutive side by 4 feet.  

Which inequality correctly compares the size of Donovan's painted area over the last two days?

Alternatives are in the graph below

Source: https://answers.yahoo.com/question/index?qid=20171204193309AAKLjwU

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Square-shaped area Donovan painted yesterday = 7x feet²

Today he painted 3 feet more on one side of the orange area and 4 feet more on the other side

2. Which inequality correctly compares the size of Donovan's painted area over the last two days?

First, we need to calculate the length of the side of the square-shaped area Donovan painted yesterday. For doing that, we use this equation:

Side of the square-shaped area Donovan painted yesterday ² = 7x feet²

Side of the square-shaped area Donovan painted yesterday  = √7x feet

Now we can use this information to calculate how much area he painted today.

One side of the area Donovan painted today = √7x + 3

Second side of the area Donovan painted today = √7x + 4

Area Donovan painted today = (√7x + 3) * (√7x + 4)

Area Donovan painted today = 7x + 3√7x + 4√7x + 12

Area Donovan painted today = 7x + 7√7x + 12 feet²

Finally, we know that the are Donovan painted today is bigger than the area Donovan painted yesterday, and we use any of these two inequalities to express it:

7x + 7√7x + 12 > 7x

7x <  7x + 7√7x + 12

This second inequality is the alternative D for solving this whole problem. The correct answer is D. 7x <  7x + 7√7x + 12

Moderator: The graph attached contains the alternatives to answer the problem.