Question

unit 1 module 2 | session 2
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date
factors & art supplies page 1 of 2
1 imagine using 48 tiles to build each rectangle. write in the missing dimensions on the rectangle sketches.
rectangles with labels 1, 2, 8, 16 and area 48; handwritten: 1×48=48, 2×24=48

Explanation:

Step1: Analyze the first rectangle (height 1)

The area of a rectangle is \( \text{length} \times \text{width} \). Here, area is 48, height (one side) is 1. So \( 1 \times \text{length} = 48 \), so length is 48.

Step2: Analyze the second rectangle (height 2)

Using area formula: \( 2 \times \text{length} = 48 \), solve for length: \( \text{length} = \frac{48}{2} = 24 \).

Step3: Analyze the rectangle with height 8

\( 8 \times \text{length} = 48 \), so \( \text{length} = \frac{48}{8} = 6 \).

Step4: Analyze the rectangle with height 16

\( 16 \times \text{length} = 48 \), so \( \text{length} = \frac{48}{16} = 3 \). (Assuming the missing dimension is length, we find factors of 48: 1×48, 2×24, 8×6, 16×3, etc.)

Answer:

For the rectangles:

• Height 1: Length = 48 (since \( 1 \times 48 = 48 \))
• Height 2: Length = 24 (since \( 2 \times 24 = 48 \))
• Height 8: Length = 6 (since \( 8 \times 6 = 48 \))
• Height 16: Length = 3 (since \( 16 \times 3 = 48 \))