What will come in the place of the question mark ‘?’ in the following question? (66)2 - (34)2 + ?2 = (60)2
20
Finding the Missing Term in the Squares Equation
This problem asks us to find the value that replaces the question mark ('?') in the given mathematical equation. The equation involves the squares of numbers.
The Equation Explained
The equation provided is:
(66)² - (34)² + ?² = (60)²
Our goal is to isolate the term with the question mark, ?², and find its value.
Step-by-Step Calculation
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Calculate the squares: First, we need to find the values of the squared terms:
- $66^2 = 66 \times 66 = 4356$
- $34^2 = 34 \times 34 = 1156$
- $60^2 = 60 \times 60 = 3600$
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Substitute the values back into the equation: Now, we replace the squared terms with their calculated values:
4356 - 1156 + ?² = 3600 -
Simplify the left side of the equation: Combine the known numbers on the left side:
(4356 - 1156) + ?² = 36003200 + ?² = 3600 -
Isolate the ?² term: To find
?², we subtract 3200 from both sides of the equation:?² = 3600 - 3200?² = 400 -
Find the value of ?: To find the value of the question mark, we need to take the square root of 400:
? = \sqrt{400}? = 20
Conclusion
The value that should replace the question mark ('?') in the equation is 20. This matches the third option provided.
Similar Questions
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Important Questions from Simplification
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