Original image here
Source: My coaching DPP (Daily Practice Paper)
I found $5^2+3^2-4^2=18,\,7^2+5^2-3^2=65.$ So, $?=8^2+6^2-5^2=75$ which is not in option. Anyone please help.
Since our dear friend balazs.com has not deigned to provide a comprehensible explanation to us lowly mortals, I've provided a simple explanation here:
The missing number is:
Not the only one missing
This is because:
You have correctly deduced the pattern for turning the outside numbers into the inside number. Specifically, the pattern adds the squares of the upper outside numbers and subtracts the square of the lower outside number to produce the inner number. As shown here:5*5 + 3*3 - 4*4 = 25 + 9 - 16 = 18 7*7 + 5*5 - 3*3 = 49 + 25 - 9 = 65The problem is that the third triangle is malformed per the available answer choices. The actual equation you're looking for is:
9*9 + 6*6 - 5*5 = 81 + 36 - 25 = 92. Therefore, the answer (central missing number) is B) 92, and the other missing number is 9, which should replace the misprinted 8 on the top left of the third triangle.