If $13^{2}$ + $a^{2}$ = $b^{2}$ ,
then a + b = .

144

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169

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196

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225

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Solution

The correct option is B 169
Since 13 is an odd number, we can form a Pythagorean triplet which will have 13 as the smallest number of the triplet.
Take the square of 13.
13 $^{2} =$ 169.
Now, divide 169 into two parts. For this divide 169 by 2.
On dividing 169 by 2, the quotient is 84.
Thus the next number is 84 + 1 = 85.
Thus the Pythagorean triplet is 13, 84, 85.
Verify that : 13 $^{2} +$ 84 $^{2} =$ 85 $^{2}$ .
Hence, a = 84 and b = 85.
So, a+b = 169.

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