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

rectangle?

Answer 1

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

Explanation:

Let the dimension of the rectangle be l and w.

A =
`24x^6y^(15)`

`24x^6y^(15)=l* w`

A) If the dimension are :

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

Area of the rectangle

`= 2x^5y^8* 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* 4x^3y^5=24x^5y^(8)\\eq A`

C) If the dimension are :

`l=10x^6y^(15),w = 14x^6y^(15)`

Area of the rectangle

`= 10x^6y^(15)* 14x^6y^(15)=140x^(12)y^(30)\\eq A`

D) If the dimension are :

`l=9x^4y^(11),w = 12x^2y^4`

Area of the rectangle

`= 9x^4y^(11)* 12x^2y^4=108x^6y^(15)\\eq A`

Answer 2

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

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)