Suppose the planned dimensions of a rectangular kitchen have a length-to-width ratio of 3 to 2. The length of the original kitchen is 6z feet. The original kitchen can be made larger by adding four feet to each original dimension. Write a polynomial expression that represents the floor area of the larger kitchen in square feet. Write your answer in standard form.

Answer:

150 sq. in.

Step-by-step explanation:
Because... Suppose the planned dimensions of a rectangular kitchen have a length-to-width ratio of 3 to 2. The length of the original kitchen is 6z feet. The original kitchen can be made larger by adding four feet to each original dimension. Write a polynomial expression that represents the floor area of the larger kitchen in square feet.

The polynomial expression that represents the floor area of the larger kitchen in square feet is  24z² + 40z + 16

The area of Rectangle is length times of width.

The length-to-width ratio of the original rectangular kitchen is 3 to 2.

Let the width of the original kitchen "w".

Then the length of the original kitchen is length = 3/2×w

We are also told that the length of the original kitchen is 6z feet. We can use this information to solve for the width of the original kitchen:

6z = 3/2×w

w = 4z

So the width of the original kitchen is 4z feet.

To make the kitchen larger, we add four feet to each original dimension. The new length is:

length = 6z + 4 feet

width = 4z + 4 feet

Area = (6z + 4 feet) × (4z + 4 feet)

Multiplying out the terms, we get:

Area = 24z² + 40z + 16 square feet

Therefore, the polynomial expression that represents the floor area of the larger kitchen in square feet is  24z² + 40z + 16

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