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.