What is the length and width of the rectangle?

Question

The rectangle below has an area of 15k⁴+35k³+20k² Square meters

 

The width of the rectangle (in metres) is equal to the greatest common monomial factor of 15k⁴, 35k³ and 20k²

 

What is the length and width of the rectangle ?

Answer 1

Hi Vik - thank you for posting this. The first step is to find the greatest common monomial factor of 15k⁴, 35k³ , and 20k²

 

The greatest common factor is the biggest number that divides evenly into each one of the numbers without a remainder...the only thing that's different about our situation is that we have variables in addition to regular number (but the same logic applies...we need to find the biggest variable that goes into k⁴ , k³ , and k² ).

 

The biggest number that goes into 15, 35 and 20 is the number 5. The biggest variable that goes into k⁴ , k³ , and k² is k²

 

Combining the number and the variable, we get that the greatest common monomial factor is 5k²

 

Since area is length x width, and we just figured out that width is 5k² , all we have to do to find length is divide 15k⁴+35k³+20k² by 5k² , and we get that the length is 3k²+7k+4

 

So the width is 5k²  and the length is 3k²+7k+4