Answer:
The correct answer is :[tex]l=2x^5y^8,w = 12xy^7[/tex]
Step-by-step explanation:
Let the dimension of the rectangle be l and w.
A = [tex]24x^6y^{15}[/tex]
[tex]24x^6y^{15}=l\times w[/tex]
A) If the dimension are :
[tex]l=2x^5y^8,w = 12xy^7[/tex]
Area of the rectangle
[tex]= 2x^5y^8\times 12xy^7=24x^6y^{15}=A[/tex]
B) If the dimension are :
[tex]l=6x^2y^3,w = 4x^3y^5[/tex]
Area of the rectangle
[tex]= 6x^2y^3\times 4x^3y^5=24x^5y^{8}\neq A[/tex]
C) If the dimension are :
[tex]l=10x^6y^{15},w = 14x^6y^{15}[/tex]
Area of the rectangle
[tex]= 10x^6y^{15}\times 14x^6y^{15}=140x^{12}y^{30}\neq A[/tex]
D) If the dimension are :
[tex]l=9x^4y^{11},w = 12x^2y^4[/tex]
Area of the rectangle
[tex]= 9x^4y^{11}\times 12x^2y^4=108x^6y^{15}\neq A[/tex]
