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

Length: 7y^2+3

Width: 10y^6

Explanation:

Given that 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.

First let us get the width;

70y^8 = 7 * 10 * y^2 * y^6

30y^6 = 3 * 10 * y^6

Since 10y^6 is common to both factors, hence the width of the rectangle will be 10y^6

Given;

Area = Length * width

A(x) = W(x)*L(x)

A(x) = 70y^8 + 30y^6

A(x) = 10y^6(7y^2+3)

On comparison

L(x) = 7y^2+3

Hence length is 7y^2+3 and width is 10y^6