Question

The area of a rectangle, A = 1 x w is represented by the expression 24x^6y^15 Which could be the dimensions of the

Answer 1

Answer:

The correct answer is :$l=2x^5y^8,w = 12xy^7$

Step-by-step explanation:

Let the dimension of the rectangle be l and w.

A = $24x^6y^{15}$

$24x^6y^{15}=l\times w$

A) If the dimension are :

$l=2x^5y^8,w = 12xy^7$

Area of the rectangle

$= 2x^5y^8\times 12xy^7=24x^6y^{15}=A$

B) If the dimension are :

$l=6x^2y^3,w = 4x^3y^5$

Area of the rectangle

$= 6x^2y^3\times 4x^3y^5=24x^5y^{8}\neq A$

C) If the dimension are :

$l=10x^6y^{15},w = 14x^6y^{15}$

Area of the rectangle

$= 10x^6y^{15}\times 14x^6y^{15}=140x^{12}y^{30}\neq A$

D) If the dimension are :

$l=9x^4y^{11},w = 12x^2y^4$

Area of the rectangle

$= 9x^4y^{11}\times 12x^2y^4=108x^6y^{15}\neq A$

Answer 2

Answer:

A. 2x^5y^8 and 12xy^7

Step-by-step explanation:

The question is on laws of indices

when we have x^a × x^b = x^(a+b)

Given in the question 24x^6y^15

24 could be 2×12............for the length and width

Then x^6 = x^1 × x^5 = x^(1+5) = x^6

And  y^15 = y^8 ×y^7 = y^(8+7) = y^(15)