Question : If the area of a square is decreased by 19%, then the diagonal of the square is decreased by:
Option 1: 10%
Option 2: 15%
Option 3: 5%
Option 4: 12%
Correct Answer: 10%
Solution :
Use: Length of a diagonal in a square = $\sqrt2$ × side of the square
Let the side of the square be 10 cm.
Area of square = 10 × 10 = 100 cm
2
Diagonal of the square = $10\sqrt{2}$ cm
Now,
Decrease in area by 19%
New area = 100 × $\frac{81}{100}$ = 81 cm
2
So, new side = $\sqrt{81}$ = 9 cm
⇒ New length of the diagonal = $9\sqrt{2}$ cm
Percentage decrease in the length of the diagonal = $\frac{\sqrt{2}}{10\sqrt{2}}$ × 100 = 10%
Hence, the correct answer is 10%.
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