Question

In the $△$ given below, find the value of x.

• A. 5
• B.
• C.
• D.

Answer 1

The correct option is D

This is a direct application of Pythagoras' theorem. One common mistake students may commit is that, since 3, 4, 5 are part of Pythagorean triplets, x will be 5. But in this case 4 is the hypotenuse. So 5 won't be part of this $△$.

If a, b and c are sides of a right -angled triangle as shown in the figure, then

$a^2$ + $b^2$ = $c^2$.

Applying the same to the triangle given in question.

$3^2$ + $x^2$ = $4^2$

$\Rightarrow$ $x^2$ = $4^2$ - $3^2$

= 7

$\Rightarrow$ x = $\sqrt{7}$(-$\sqrt{7}$ can't be length)

Key steps/concepts : Pythagoras's theorem.