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Question

Difficulty: EasyArea of Two-Dimensional Shapes

A square picture has an area of 1616 square inches. If the side length of the picture is doubled, what is the area, in square inches, of the new picture?

  1. A
    88
  2. B
    3232
  3. 6464Answer
  4. D
    128128

Answer

6464 square inches
The area of a square with side length ss is given by s2s^2. Since the original area is 1616 square inches, the original side length is 16=4\sqrt{16} = 4 inches. Doubling this side length gives a new side length of 88 inches. Therefore, the area of the new square is 82=648^2 = 64 square inches. Alternatively, when all linear dimensions of a two-dimensional shape are multiplied by a scale factor kk, the area is multiplied by k2k^2. Since the side length is doubled (k=2k = 2), the area is multiplied by 22=42^2 = 4, resulting in 16×4=6416 \times 4 = 64 square inches.

Step-by-Step Solution

1
Determine the side length of the original square.
The side length is 16=4\sqrt{16} = 4 inches.
The area of a square is given by A=s2A = s^2, where ss is the side length. So, s=As = \sqrt{A}.
2
Calculate the side length of the new square after doubling.
The new side length is 4×2=84 \times 2 = 8 inches.
The problem states that the side length is doubled.
3
Calculate the area of the new square.
The new area is 82=648^2 = 64 square inches.
The area of the new square is the square of its new side length (8 inches×8 inches8 \text{ inches} \times 8 \text{ inches}).

Key Concept

When a two-dimensional shape is scaled by a factor of kk, its area is scaled by a factor of k2k^2.
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Topics

Area of Two-Dimensional Shapes

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