MCQ
If $\triangle \text{ABC}$ is an isosceles right-triangle right angled at C such that $AC = 5cm.$ Then, $AB =$
  • A
    $2.5cm$
  • $5\sqrt{2}\text{cm}$
  • C
    $10 cm$
  • D
    $5 cm$

Answer

Correct option: B.
$5\sqrt{2}\text{cm}$


Suppose $BC$ is the ladder which is placed againts the wall $OA$. The foot of the ladder $C$ is $15m$ away from the foot $O$ of the wall and its top reaches the window which is $20m$ above the ground.
In right traingle $ABC$
$AB^2 = BC^2 + AC^2$
$\Rightarrow AB^2 = (5)^2 + (5)^2$
$\Rightarrow AB^2 =25 + 25$
$\Rightarrow AB^2 = 50$
$\Rightarrow \text{AB}^2=(5\sqrt{2})^2$
$\Rightarrow \text{AB}=5\sqrt{2}\text{cm}$
Hence, the correct answer is option (b).

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