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Q.

The length of an aluminum strip is 40cm. If the lengths in cm are measured in natural numbers, the measurement of all the possible rectangular frames which can be made out of it is


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a

1 cm×19 cm, 2cm×18 cm, 3cm×17 cm, 4cm×16 cm, 5cm×15 cm, 6cm×14 cm, 7cm×13 cm, 8cm×12 cm, 10cm×10 cm

b

1 cm×19 cm, 2cm×18 cm, 3cm×17 cm, 4cm×16 cm, 5cm×15 cm, 6cm×14 cm, 7cm×13 cm, 8cm×12 cm, 9cm×11 cm, 10cm×10 cm

c

1 cm×19 cm, 2cm×18 cm, 4cm×16 cm, 5cm×15 cm, 6cm×14 cm, 7cm×13 cm, 8cm×12 cm, 9cm×11 cm, 10cm×10 cm

d

1 cm×19 cm, 4cm×16 cm, 5cm×15 cm, 6cm×14 cm, 7cm×13 cm, 8cm×12 cm, 9cm×11 cm, 10cm×10 cm 

answer is B.

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Detailed Solution

Given that length of an aluminum strip = 40 cm.
According to the given condition,
The aluminum strip is used to make the rectangular frames.
Then,
Length of the aluminum wire = Perimeter of the rectangle
Rectangular frame of length = 15 cm
Rectangular frame of breadth = 5cm.
Perimeter of the rectangle frame = length of the aluminum strip
⇒2 × (length + breadth) = 40
⇒ (l + b) = 402 ⇒(l + b) = 20
The possible measurement of rectangular frames are 1 cm×19 cm, 2cm×18 cm, 3cm×17 cm, 4cm×16 cm, 5cm×15 cm, 6cm×14 cm, 7cm×13 cm, 8cm×12 cm, 9cm×11 cm, 10cm×10 cm.
Hence, option (2) is correct.
 
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The length of an aluminum strip is 40cm. If the lengths in cm are measured in natural numbers, the measurement of all the possible rectangular frames which can be made out of it is