Question

Question 2

Answer 1

Answer:

Please check the explanation.

Step-by-step explanation:

Calculating the area of the outer rectangle:

Given

• The length outer rectangle = l = 3x - 1

• The width of outer rectangle = w = 5x + 2

Thus,

The area of the outer rectangle:

$A = wl$

    $= (5x + 2) (3x - 1)$

    $=5x\cdot \:3x+5x\left(-1\right)+2\cdot \:3x+2\left(-1\right)$

     $=5\cdot \:3xx-5\cdot \:1\cdot \:x+2\cdot \:3x-2\cdot \:1$

      $=15x^2+x-2$

Calculating the area of the inner rectangle:

Given

• The length inner rectangle = l = x + 7

• The width of inner rectangle = w = x

Thus,

The area of the outer rectangle:

A = wl

   = x(x+7)

   = x² + 7

Calculating the area of the shaded region:

As

The area of the outer rectangle = 15x² + x - 2

The area of the inner rectangle = x² + 7

• The area of the shaded region can be determined by subtracting the area of the inner rectangle from the area of the outer rectangle.

Thus,

shaded region Area = Outer Rectangle Area - Inner Rectangle Area

                                  = 15x² + x - 2 - (x² + 7)

                                   =  15x² + x - 2 - x² - 7

                                   = 14x² + x - 9

Therefore, the Area of the shaded region is: 14x² + x - 9