Question

For exercises 66-69, write equivalent expressions to show two different ways to find the area of each rectangle. use the ideas of the distributive property.

option a) (w + h)^2; 2(w × h)
option b) (w - h)^2; (w + h)^2
option c) (w × h) + (w × h); w(h + h)
option d) w^2 + h^2; w^2 - h^2

Answer 1

Option C represents two equivalent expressions for the area of a rectangle: (w × h) + (w × h) and w(h + h), both representing twice the rectangle's area.

Step-by-step explanation:

The question is asking for equivalent expressions to find the area of a rectangle, using the distributive property. To find the area of a rectangle, you multiply its width (w) by its height (h), which gives you the formula A = w × h. Now, let's evaluate the options:

• Option A: (w + h)^2 is not an expression for the area of a rectangle, nor is 2(w × h) using the distributive property correctly.
• Option B: (w - h)^2 is also not correct, and (w + h)^2 does not represent the area of a rectangle.
• Option C: (w × h) + (w × h) can be seen as w×h twice, which is the same as 2(w × h), and w(h + h) is equivalent because it uses the distributive property to double the height before multiplying by the width, which also results in 2(w × h), representing twice the rectangle's area.
• Option D: w^2 + h^2 and w^2 - h^2 do not represent the area of a rectangle.

Correct Answer: Option C, which provides two equivalent ways to express twice the area of a rectangle either by summing two areas (w × h) + (w × h) or using the distributive property w(h + h).