plz solve this question
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plz solve this question
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Answer :
l = 12 , b = 5
Solution :
Given : l + b = 17 , l² + b² = 169
To find : l = ? , b = ?
We have ,
l + b = 17 -------(1)
l² + b² = 169 --------(2)
We know that ,
(A + B)² = A² + B² + 2•AB
Thus ,
=> (l + b)² = l² + b² + 2•lb
=> 17² = 169 + 2•lb
=> 289 = 169 + 2•lb
=> 2•lb = 289 - 169
=> 2•lb = 120
=> lb = 120/2
=> lb = 60
Also ,
We know that ,
(A - B)² = (A + B)² - 4•AB
Thus ,
=> (l - b)² = (l + b)² - 4•lb
=> (l - b)² = 17² - 4•60
=> (l - b)² = 289 - 240
=> (l - b)² = 49
=> l - b = √49
=> l - b = 7 --------(3)
Now ,
Adding eq-(1) and (3) , we get ;
=> l + b + l - b = 17 + 7
=> 2•l = 24
=> l = 24/2
=> l = 12
Now ,
Putting l = 12 in eq-(1) , we get ;
=> l + b = 17
=> 12 + b = 17
=> b = 17 - 12
=> b = 5
Hence ,
l = 12 , b = 5