Question : Let $ABC$ and $PQR$ be two congruent right-angled triangles such that $\angle A=\angle P=90^{\circ}$. If $BC=13\ \text{cm}$ and $PR=12\ \text{cm}$, then find the length of $AB$.
Option 1: 25 cm
Option 2: 20 cm
Option 3: 10 cm
Option 4: 5 cm
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Correct Answer: 5 cm
Solution :
Given: $\angle A=\angle P=90^{\circ},BC$ = 13 cm and $PR= 12\ \mathrm{cm}$
Given: triangles $ABC\cong PQR$
Now in $\triangle ABC$,
$BC$ = 13 cm
$AC$ = 12 cm ($AC=PR$ because of congruent triangles)
Applying Pythagoras theorem,
$BC^2=AC^2+AB^2$
⇒ $13^2=12^2+AB^2$
$\therefore AB$ = 5 cm
Hence, the correct answer is 5 cm.
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