the length of a rectangle is 3 inches greater than the width write a polynomial that reoresent the area of the rectangle

Question

find the area of the rectangle when the width is 4 inches

Answer 1

Length of a rectangle is 3 inches greater than the width, so:

 

L = W + 3

 

Area of a rectangle: 

 

A = L x W

 

A = ( W + 3 ) x W

 

A = W² + 3 W ----------------- Polynomial representing area of the rectangle in terms of Width.

 

Substitute W = 4 to find the area of the rectangle.

 

A = 4² + 3 (4)

 

A = 16 + 12

 

A = 28 inch² 

 

L = W + 3

 

L = 4 + 3

 

L = 7 inches

 

 

Answer 2

For this question, you're going to say that width is x. Therefore, length will be x+3. 

 

Formula for area of a rectangle is width times length. So you will multiply x with (x+3). Using the foil method, you will get x^2 + 3x. 

 

There are two ways to find the area when the width is given.

 

If you know that width, which is x, is 3. Than length, which x+3 will be 3+3. Which will be 6. Area will be width times length which will be: 3x6 = 18 inches^2

 

The other method: You have come up with a polynomial. The polynomial is x^2 + 3x and you already designated x as the width. Since width is 3, you can substitute 3 in the place of x. Which will be 3^2 + 3(3) = 18 inches^2

 

Knowing two methods is helpful in math problems because you now have alternative ways to check you answer. 

 

I hope this helps!