Question

The rectangle below has an area of 70y^8+30y^6.The width of the rectangle 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

Answer:

Width $10y^6$ units

Length $7y^2+3$ units

Step-by-step explanation:

The rectangle has an area of $70y^8+30y^6.$

The width of the rectangle is equal to the greatest common monomial factor of $70y^8$ and $30y^6.$ Find this monomial factor:

$70y^8=2\cdot 5\cdot 7\cdot y^8\\ \\30y^6=2\cdot 3\cdot 5\cdot y^6\\ \\GCF(70y^8,30y^6)=2\cdot 5\cdot y^6=10y^6$

Hence, the width of the rectangle is $10y^6$ units.

The area of the rectangle can be rewritten as

$10y^6(7y^2+3).$

The area of the rectangle is the product of its width by its length, then the length of the rectangle is $7y^2+3$ units.