Question

9 Ron's family plans to add a new room to their house. They initially planned the width and the length of the room to be 10 feet and 25 feet. Now they want to add to the width. The amount they want to add to the width is shown by the variable I. 25 101 + Ron thinks that the area of the room will be 250 + 257. Is he correct? Why or why not? Select all that apply. A Yes, because the area of the room is the sum of 25.10 and 25r. No, because the area of the room is the sum of 25 . 10 and I. No, because the area of the room is the product of 25 + 10 and 25.1. D Yes, because the area of the room is the product of 25 and 10+ I.

Answer 1

The room is a rectangle with dimensions 25 and x + 10. The area of a rectangle is the product of its dimensions, so the area will be:

`25\cdot(x+10)`

We have to add the parenthesis because we first need to add 10 and x and then multiply. Distributing the 25, we have:

`25\cdot(x+10)=25\cdot x+25\cdot10=25x+250=250+25x`

As we can see, this matches what Ron thinks the area will be, so he is correct. Thus, the answer is "Yes". The why can be both because the area is the sum of 25*10 and 25x and because the area is the product of 25 and 10 + x.

So, the correct alternatives are A and D.