Question

Choose the correct option for 'a' and 'b' respectively from those given below: ${10}^2$ + $a^2$ = $b^2$

• A. 25, 26
• B. 24, 26
• C. 22, 23
• D. 23, 24

Answer 1

The correct option is B 24, 26

Applying the short cut method, we can calculate the values of a and b as follows:
Divide the given even number 10 by 2 to get an odd number.
Hence $\frac{10}{2}$ = $5$ .
Next we know $5^2$ = 25.
The 2 consecutive numbers that add up to 25 = 12 and 13.

Hence $5^2+{12}^2={13}^2$
Now multiplying all the bases by 2 (since 5 x 2 = 10) we get
${10}^2+{24}^2={26}^2$
Verifying the answer: 100 + 576 = 676.