Suppose The Area Of A Rectangle Is (6x2 20137x + 14) Square Units. If Its Width Is (2x 2013 5) Units, What Expression Represents Its Length? How About

Suppose the area of a rectangle is (6x2 –7x + 14) square units. If its width is (2x – 5) units, what expression represents its length? How about its perimeter?

 

Area of the Rectangle:

Perimeter of the Rectangle:

      The length of the rectangle is represented by the expression 3x + 4 while the perimeter is 10x - 2.  

Solution:

1. Given: Area of the Rectangle = 6x² - 7x + 14

             width of the rectangle = 2x - 5

2. Using A = lw then,

6x² - 7x + 14 = l (2x - 5)

3. Divide both sides of the equation by 2x - 5 to find for the length.

6x² - 7x + 14 = l (2x - 5)

    2x - 5           2x - 5

4. By long division,  

          3x + 4 _____

2x - 5√6x² - 7x + 14

           6x² - 15x ___

                   8x + 14

                   8x -  20

                           34

5. To check, multiply 2x – 5 with 3x + 4 then add 34 which is the remainder.

(2x – 5)(3x + 4) + 34 = 6x² - 7x + 14

6x² + (8x – 15x)+ (-20 + 34) = 6x² – 7x + 14

6x² – 7x + 14 = 6x² – 7x + 14

6. Using l = 3x + 4 and w = 2x – 5, find the perimeter.

P = 2l + 2w

P = 2(3x + 4) + 2(2x – 5)

P= 6x + 8 + 4x – 10

P = (6x + 4x) + (8 + (-10))

P = 10x – 2

Code:  10.3.1.2.1

For more information regarding areas of the rectangle, go to links:

brainly.ph/question/110308

brainly.ph/question/2004152

For more information regarding perimeter of the triangle, go to link:

brainly.ph/question/245745


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