Answer:

1.) To find the area of the rectangle, just multiply its length to its width. Which is :

A = l × w

A = (2x + 3) × (3x - 5)

Use the Foil Method to simplify the equation.

A = 2x(3x) + 2x(-5) + 3(3x) + 3(-5)

A = 6x² - 10x + 9x - 15

A = 6x² - x - 15

Therefore, the area of our rectangle is (6x² -x - 15) square units.

2.) The area of our square is simple s². Since the sides of a square are equal, we have :

A = s²

A = (2x + 7)²

Perform the Square of a Binomial Method to simplify the equation

A = (2x)² + 2(2x)(7) + (7)²

A = 4x² + 2(14x) + 49

A = 4x² + 28x + 49

Therefore, the area of our square is (4x² + 28x + 49) square units.

3.) To find the length of our rectangle, we just need to simply divide the width to its area. In equation, we have :

l = \frac{6x^{2} + 13x - 5 }{2x + 5}l=

2x+5

6x

2

+13x−5

Now, we need to factor out our dividend so we can cancel out like terms.

\begin{gathered}l = \frac{6 {x}^{2} + 13x - 5 }{2x + 5} \\ l = \frac{(3 {x} - 1)(2x + 5 )}{2x + 5} \end{gathered}

l=

2x+5

6x

2

+13x−5

l=

2x+5

(3x−1)(2x+5)

Now, we can observe that we have two 2x + 5. We will cancel that. And we have our answer as:

l = 3x - 1l=3x−1

Therefore, the length of our rectangle is 3x - 1

Sana po makatulong:)