# The area of a rectangle of length x is given by 3x2 +5x. Find the

width of the rectangle.

The area of a rectangle with width t is given by 33t - t 2. Factor the

expression and determine the length of the rectangle in terms of t

length times width=area, so factor out an x to get the width. reverse it foe the second one

## To find the width of the rectangle, we need to factor the quadratic expression 3x^2 + 5x, which represents the area of the rectangle.

Step 1: Identify the common factor, if any.

In this case, there is a common factor of x in both terms: x(3x + 5).

Step 2: Write down the factored form.

The factored expression for the area of the rectangle, which represents the length times width, is x(3x + 5).

Therefore, the width of the rectangle is 3x + 5.

Now, let's move on to the second question.

To find the length of the rectangle in terms of t, we need to factor the quadratic expression 33t - t^2, which represents the area of the rectangle with width t.

Step 1: Rearrange the terms.

The quadratic expression can be rearranged as -t^2 + 33t.

Step 2: Factor out the common factor.

In this case, there is a common factor of -t: -t(t - 33).

Step 3: Write down the factored form.

The factored expression for the area of the rectangle, which represents the length times width, is -t(t - 33).

Therefore, the length of the rectangle in terms of t is t - 33.