Answer:
The length of rectangle is (3a+2).
Step-by-step explanation:
The area of rectangle is [tex]12a^2-a-6[/tex].
The width of the triangle is (4a-3).
The area of a rectangle is the product of its length and width.
[tex]A=l\times w[/tex]
[tex]12a^2-a-6=l\times (4a-3)[/tex]
[tex]l=\frac{12a^2-a-6}{4a-3}[/tex]
[tex]l=\frac{12a^2-9a+8a-6}{4a-3}[/tex]
[tex]l=\frac{3a(4a-3)+2(4a-3)}{4a-3}[/tex]
[tex]l=\frac{(4a-3)(3a+2)}{4a-3}[/tex]
Cancel out the common factor 4a-3.
[tex]l=3a+2[/tex]
Therefore the length of the rectangle is (3a+2).
