MCQ
$\triangle\text{ABC}$ is an isosceles triangle in which $\angle\text{C}=90^\circ$ If $AC = 6\ cm$, then $AB =$
- A$6\sqrt{2}\text{cm}.$
- B$6\text{cm}.$
- C$2\sqrt{6}\text{cm}.$
- ✓$4\sqrt{2}\text{cm}.$
✓
Answer
Correct option: D.
$4\sqrt{2}\text{cm}.$
$\triangle\text{ABC}$ is an isosceles with $\angle\text{C}=90^\circ$
$AC = BC$
$AC = 6cm$
$AB^2 = AC^2 + BC^2 ($Pythagoras Theorem$)$
$(6)^2 + (6)^2 = 36 + 36 = 72 (AC = BC)$
$\text{AB}=\sqrt{72}=\sqrt{(36\times2}=6\sqrt{2}\text{cm}.$
$AC = BC$
$AC = 6cm$
$AB^2 = AC^2 + BC^2 ($Pythagoras Theorem$)$
$(6)^2 + (6)^2 = 36 + 36 = 72 (AC = BC)$
$\text{AB}=\sqrt{72}=\sqrt{(36\times2}=6\sqrt{2}\text{cm}.$
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