Question

If $24,x,26$ form a pythagorean triplet,
then $x=?$.

• A. $10$
• B. $5\sqrt{2}$
• C. $25$
• D. $4\sqrt{7}7$

Answer 1

The correct option is A $10$

$\text{We know that,}2m,m^2-1\text{and}{m}^2+1\text{form a Pythagorean triplet.}$

$\text{Let us consider}(m^2–1)=24\Rightarrow m^2=24+1\Rightarrow m^2=25\Rightarrow m=5\text{Then,}(m^2+1)=25+1=26$

$\text{Hence,}x=2m$
$\therefore x=2\times 5=10$

$\text{Lets verify}\Rightarrow {10}^2+{24}^2=100+576=676\Rightarrow {26}^2=676\therefore {10}^2+{24}^2={26}^2$

$\text{24, 10, 26 form a Pythagorean triplet.}$
$\therefore x=10$