Question

Elle and heather drew floor models of there living rooms.Elles model respresented 20 feet by 15 feet.Heathers model respresented 18 by 18 feet. Whose floor model represents the greater area? How much greater? Show your work

Answer 1

• Heather's model represents the greater area.
• 
  `24\ ft^2` greater.

Explanation:

The formula for calculate the area of a rectangle is:

`A=lw`

Where "l" is the lenght of the rectangle and "w" is the width.

The formula for calculate the area of a square is:

`A=s^2`

Where "s" is the side lenght.

In this case, knowing that Elle's model represented 20 feet by 15 feet, we can say that:

`l=20\ ft\\w=15\ ft`

Therefore, substituting these values into the formula
`A=lw`, we get that the area is:

`A_1=(20ft)(15ft)=300\ ft^2`

Since Heather's model represented 18 ft by 18 feet, we can identify that:

`s=18ft`

Substituting this value into
`A=s^2`, we get this area:

`A_2=(18ft)^2=324\ ft^2`

Notice that Heather's model represents the greater area.

To calculate how much greater it is, subtract the areas. Then:

`324\ ft^2-300\ ft^2=24\ ft^2`