Question

The rectangle below has an area of 6n^4+20n^3+14n^26n 4 +20n 3 +14n 2 6, n, start superscript, 4, end superscript, plus, 20, n, cubed, plus, 14, n, squared.The width of the rectangle is equal to the greatest common monomial factor of 6n^4, 20n^3,6n 4 ,20n 3 ,6, n, start superscript, 4, end superscript, comma, 20, n, cubed, comma and 14n^214n 2 14, n, squared.What is the length and width of the rectangle?

Answer 1

Width of Rectangle = 2n² & Length of Rectangle = 3n² + 10n  + 7

Step-by-step explanation:

Area of Rectangle  =6n⁴  + 20n³   + 14n²  

= 2n² ( 3n² + 10n  + 7)

= 2n² (3n² + 3n + 7n + 7)

= 2n² (3n(n + 1) + 7(n+1))

= 2n² (n+1)(3n + 7)

Width of the rectangle is equal to the greatest common monomial factor of 6n⁴, 20n³  & 14n²

6n⁴ = 2n² * 3n²

20n³ = 2n² * 10n

14n² = 2n² * 7n

greatest common monomial factor = 2n²

Width of Rectangle = 2n²

Length of Rectangle =  2n² (n+1)(3n + 7) /2n²

= (n+1)(3n + 7)

= 3n² + 10n  + 7

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