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
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