Question

Sadie computes the perimeter of a rectangle by adding the length, I, and width, w, and doubling this sum. Eric computes the perimeter of a rectangle by doubling the length, I, doubling the width, w, and adding the doubled amounts. Explain why Sadie and Eric always get the same answer, no matter what the length and width of the rectangle are. plz help i really need it I need to turn this in tomorrow. Help plz

Answer 1

Due to the distributive property the expression are the same.

Explanation:

Sadie expression is "perimeter = 2*(length + width)", while Eric's is "perimeter = 2*length + 2*width". The value for both is always the same for any rectangle, because the expressions are the same due to the distributive property. To prove this we will expand Sadie's expression as shown below:

perimeter = 2*(length + width)

perimeter = 2*length + 2*width

Which is the same as Eric's.