The length of a rectangular garden is represented by 3x4 and the width is represented by 2x-5. Which of the following represents the total area of the garden?
A) 5x-9
B) 6x + 20
C) 6x^2 -23x + 20
D) 6x^2-14x-9
The area of a rectangle is calculated by multiplying the length and the width.
So, the total area of the garden is (3x+4)(2x-5).
To simplify this expression, we can use the distributive property:
(3x+4)(2x-5) = (3x)(2x) + (3x)(-5) + (4)(2x) + (4)(-5)
= 6x^2 - 15x + 8x - 20
= 6x^2 - 7x - 20
Therefore, the total area of the garden is represented by option D) 6x^2 - 14x - 9.