If a rectangle's length is doubled and width remains the same, what happens to its area?

If a rectangle's length is doubled and width remains the same, what happens to its area?

• A. It halves
• B. It doubles
• C. It remains the same
• D. It quadruples

Answer: (B)

When the length of a rectangle is doubled while the width remains unchanged, the area of the rectangle changes accordingly. The area of a rectangle is calculated by multiplying its length by its width. If we denote the original length as \(L\) and the width as \(W\), the area can be expressed as: \[ \text{Area} = L \times W \] If the length is doubled, the new length becomes \(2L\), so the new area can be expressed as: \[ \text{New Area} = (2L) \times W = 2(L \times W) \] This shows that the new area is twice the original area, meaning that the area doubles. Therefore, when the length of the rectangle is doubled with the width remaining the same, the area effectively doubles as well. This illustrates how alterations to dimensions of geometric shapes directly impact their area, reinforcing key concepts in understanding the relationship between length, width, and area in rectangles.

When the length of a rectangle is doubled while the width remains unchanged, the area of the rectangle changes accordingly. The area of a rectangle is calculated by multiplying its length by its width. If we denote the original length as (L) and the width as (W), the area can be expressed as:

[ \text{Area} = L \times W ]

If the length is doubled, the new length becomes (2L), so the new area can be expressed as:

[ \text{New Area} = (2L) \times W = 2(L \times W) ]

This shows that the new area is twice the original area, meaning that the area doubles. Therefore, when the length of the rectangle is doubled with the width remaining the same, the area effectively doubles as well. This illustrates how alterations to dimensions of geometric shapes directly impact their area, reinforcing key concepts in understanding the relationship between length, width, and area in rectangles.