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Constructions — MATHS STD 7 — Question

Gujarat BoardEnglish MediumSTD 7MATHSConstructions1 Mark
MCQ
Mark $(\checkmark)$ against the correct answer: $\triangle\text{ABC},$ is an isosceles right triangle in which $\angle\text{A}=90^\circ$ and $BC = 6\ cm.$ Then $AB = ?$
  • A
    $2\sqrt{2}\text{cm}$
  • ✓
    $3\sqrt{2}\text{cm}$
  • C
    $4\sqrt{2}\text{cm}$
  • D
    $2\sqrt{3}\text{cm}$
✓

Answer

Correct option: B.
$3\sqrt{2}\text{cm}$

Here, $A B=A C$
In right angled isoceles triangle:
$\mathrm{BC}^2=\mathrm{AB}^2+\mathrm{AC}^2$
$\Rightarrow \mathrm{BC}^2=2 \mathrm{AB}^2$
$\Rightarrow 36=2 \mathrm{AB}^2$
$\Rightarrow \mathrm{AB}=\frac{36}{2}$
$\Rightarrow \mathrm{AB}=\sqrt{18}$
$\Rightarrow \mathrm{AB}=3 \sqrt{2} \mathrm{~cm}$

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