A) The factored form of area of rectangle is 2(2y + 5)
B) length of rectangle is 2 and width is 2y + 5 and one possible set of dimensions of rectangle is length 2 and width 7
Solution:
Given that area of rectangle is 4y + 10
A. Represent the area of the rectangle in factored form
The factored form is a parenthesized algebraic expression.
Factored form is a product of sums of products or a sum of products of sums
Given area of rectangle is 4y + 10
Taking 2 as common,
4y + 10 = 2(2y + 5)
Therefore, the factored form of given area of rectangle is 2(2y + 5)
B. Use the factored form to give one possible set of dimensions for this rectangle
The area of a rectangle is given by the formula:
area of rectangle = length x width
Therefore, area of rectangle = 2(2y + 5)
So the length of rectangle is 2 and width is 2y + 5
Or the length of rectangle is 2y + 5 and width is 2
If y = 1, then one possible set of dimensions of rectangle is:
length = 2 and width = 2(1) + 5 = 7
So one possible set of dimensions of rectangle is length 2 and width 7