Question

The rectangle below has an area of 70y^8+30y^670y 8 +30y 6 70, y, start superscript, 8, end superscript, plus, 30, y, start superscript, 6, end superscript square meters. The width of the rectangle (in meters) is equal to the greatest common monomial factor of 70y^870y 8 70, y, start superscript, 8, end superscript and 30y^630y 6 30, y, start superscript, 6, end superscript. What is the length and width of the rectangle?

Answer 1

Answer:

The width of the rectangle with area 70y⁸+ 30y⁶is 10y⁶.

The length of the rectangle with area 70y⁸+ 30y⁶ is (7y²+3).

Step-by-step explanation:

Monomial: Monomial is an algebraic expression which is consisting  of only one term.

Binomial: Binomial is an algebraic expression which is consisting  of two terms.

Trinomial: Trinomial is an algebraic expression which is consisting of three terms.

The area of a rectangle is= Length× width

Given that,

The area of the rectangle is

=70y⁸+30y⁶

70y⁸=7×5×2×y×y×y×y×y×y×y×y

30y⁶=5×3×2×y×y×y×y×y×y

The common factors of 70y⁸ and 30y⁶ are = 5,2,y,y,y,y,y,y

The greatest common factor of 70y⁸ and 30y⁶ is

=5×2×y×y×y×y×y×y

=10y⁶

∴70y⁸+ 30y⁶

= 10y⁶(7y²+3)

The greatest common monomial of 70y⁸+ 30y⁶ is 10y⁶.

Given that,

The greatest common monomial factor of 70y⁸+ 30y⁶ is equal to the width of the rectangle.

The width of the rectangle with area 70y⁸+ 30y⁶is 10y⁶.

Then the length of the rectangle with area 70y⁸+ 30y⁶ is (7y²+3).

[ area = length × width]