Question

A rectangle has a perimeter of 9x^2 - 4x. A side was removed to make a triangle.

Find the perimeter of the triangle using the expression below: (9x^2 - 4x) - (5x^2 - 3x)

a. 4x^2 - 7x
b. 4x^2 + 7x
c. 4x^2 - x
d. 4x^2 + x

Answer 1

To find the perimeter of the triangle after one side of the rectangle is removed, we start with the perimeter of the rectangle given by \(9x^2 - 4x\) and subtract the side that has been removed, given by \(5x^2 - 3x\).

We perform the subtraction of the expressions:

\[
\text{Perimeter of the triangle} = (9x^2 - 4x) - (5x^2 - 3x)
\]

Let's distribute the negative sign through the second expression:

\[
= 9x^2 - 4x - 5x^2 + 3x
\]

Now, we combine like terms:

1. Combine the \(x^2\) terms:
\[
9x^2 - 5x^2 = 4x^2
\]

2. Combine the \(x\) terms:
\[
-4x + 3x = -x
\]

Putting it all together, we find:

\[
\text{Perimeter of the triangle} = 4x^2 - x
\]

Thus, the correct answer is:

**c. \(4x^2 - x\)**.