Question

The triangle $DEF$ is right-angled triangle, right-angled at vertex $E$. The relation among the three sides of triangle $DEF$ is given as -

• A. $D{F}^2=D{E}^2+E{F}^2$
• B. $E{F}^2=D{E}^2+D{F}^2$
• C. $D{E}^2=D{F}^2+E{F}^2$
• D. $D{F}^2=D{E}^2-E{F}^2$

Answer 1

The correct option is A $D{F}^2=D{E}^2+E{F}^2$

We know,
According to Pythagoras Theorem,"In any right angled triangle, the square of hypotaneous is equal to sum of squares of base and altitude".


In the above triangle, i.e., $△DEF$ we know $\angle E={90}^o$
$\therefore$ The opposite side $DF$ is the hypotaneous of the triangle, and $DE$ and $EF$ are either base or altitude.

So the relationship is,
$D{F}^2=D{E}^2+E{F}^2$.
Hence, option $\left(a\right)$ correct.