What is the length and width of the rectangle?

Question

The rectangle below has an area of 70y^8+30y^6 square meters. The width of the rectangle (in meters) is equal to the greatest common monomial factor of 70y^8 and 30y^6. What is the length and width of the rectangle?

Answer 1

The total are of the rectangle A = 70 y⁸ + 30 y⁶

the width w = Greatest common factor of ( 70 y⁸ , 30 y⁶) = 5 y⁶ , the greatest common factor of 70 and 30 is 5

and the greatest common factor of y⁸ and y⁶ is y⁶

the area of the rectangle is A = l x w, the length l = A / w = (70 y⁸ + 30 y⁶) / 5 y⁶ = 14 y² + 6

Proof: A = l x w = (14 y² + 6) ( 5 y⁶ ) = 70 y⁸ + 30 y⁶

Answer 2

The greatest common monomial factor is 10y⁶ = width and length then is (7y² + 3); the product of these 2 terms is the area!