If the length of a rectangle is doubled and the width remains the same, how does the area change?

When the length of a rectangle is doubled while the width remains unchanged, the area is affected directly by the change in length. The area of a rectangle is calculated using the formula: Area = Length × Width.

If we start with a rectangle having a length of L and a width of W, the initial area can be expressed as:

Initial Area = L × W.

When the length is doubled, the new length becomes 2L. The width still remains W, so the new area can be calculated as:

New Area = 2L × W.

Now, we can compare the new area to the original area:

New Area = 2L × W = 2(L × W) = 2 × Initial Area.

From this, we see that the new area is indeed twice the original area, which means that the area doubles when the length is doubled and the width remains constant. Therefore, the correct conclusion is that the area doubles.