If the diagonal of a square is increased by 4 cm, its area increases by 56 cm2 . Find the ratio of the new area of the square to the initial area of the square.
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Correct answer: A
Explanation
The correct answer is Option 1 i.e. 16 : 9.
Let the side of the square be a cm, then initial area of the square = a2
Initial diagonal of the square = a√2 cm
Now we can see that area = (diagonal/√2)2
When diagonal increased by 4, i.e. a√2 + 4, area increases by 56
New Area = ((a√2 + 4)/√2)2
⇒ a2 + 56 = (a + 2√2)2
⇒ a2 + 56 = a2 + 8 + 4√2a
⇒ 4√2a = 48
⇒ a = 12/√2
Now Initial Area = a2 = 72 cm2
New area = 72 + 56 = 128 cm2
Required ratio = 128 : 72 = 16 : 9