A magic rectangular piece of cloth always shrinks its length to 1/2 and width to
1/3 whenever its owner wishes something. After three such wishes, its surface was
4 cm2. If original width is 9 cm select the option that indicates its original length in cm.
Answers
Answer:
The original length of magic rectangular piece of cloth is 96 cm
Step-by-step explanation:
Let the width of the rectangle be w and the length be l.
In the first wish, the length and the width shrink to:
Length = 1/2l
width 1/3w
Second wish
Length = 1/2 × 1/2 = 1/4l
Width = 1/3 × 1/3 = 1/9w
third wish
Length = 1/2 × 1/4 = 1/8l
Width = 1/3 × 1/9 = 1/27w
The original width of the rectangle = 9 cm
The width of the rectangle after the third wish = 1/27 × 9 = 1/3 cm
Area of the rectangle after the third wish = 1/8l × 1/3
Area = 1/24 l
From the question, the area of the magic rectangle after the third wish is given as 4 cm²
Equating the two we have:
1/24 l = 4
l = 24 × 4
l = 96 cm
the original length of the rectangular piece of cloth is 96 cm
The original length of magic rectangular piece of cloth is 96 cm.
Step-by-step explanation:
Let the original length of the cloth = L
Let the original width of the cloth = W = 9 cm (given)
After 1 wish:
New length = 1/2 × L
New width = 1/3 × 9
After 3 wish:
New length = 1/2 × 1/2 × 1/2 × 1/2 × L
New width = 1/3 × 1/3 × 1/3 × 1/3 × 9
Area of magic cloth after 3 wish = 4 cm²
Now, the area of magic cloth after 3 wish is:
4 = Length × Width
4 = 1/2 × 1/2 × 1/2 × 1/2 × L × 1/3 × 1/3 × 1/3 × 1/3 × 9
4 = L/8 × 9/27
4 = L/24
L = 4 × 24 = 96 cm