The area of a rectangle is 15 + 5y square feet. Which of the following expressions could be the lengths of the sides of the rectangle, in feet?
don't know the choices, but since 5 is the only divisor, I'd say
5 and y+3
to Steve these are the choices
A.
5 and 3y
B.
5 and 3 + y
C.
5 and 5 + y
D.
3 and 5 + 3y
well, I guess you know which one to choose, eh?
87
To determine the possible lengths of the sides of the rectangle, we need to look for expressions that can be multiplied together to give the area of the rectangle, which is given as 15 + 5y square feet.
Let's represent the length of the rectangle as "x" and the width as "y". We know that the area of a rectangle is given by the formula length × width. Therefore, we can write the equation as:
x × y = 15 + 5y
Now, let's consider the answer choices and see if any of them can be multiplied to give the expression 15 + 5y.
a) (3)(5 + 1) = 18
b) (5)(3 + y) = 15 + 5y
c) (2)(7 + 3y) = 14 + 6y
d) (4)(3 + 2y) = 12 + 8y
By comparing the expressions from the answer choices with the area equation, we can see that option b) (5)(3 + y) is the only one that matches the given expression for the area of the rectangle, which is 15 + 5y.
Therefore, the possible lengths of the sides of the rectangle are 5 feet and (3 + y) feet.