MCQ
The sides of a right angled triangle are in arithmetic progression. If the triangle has area $24$ , then what is the length of its smallest side ?
- A$4$
- ✓$6$
- C$7$
- D$8$
$\Rightarrow \quad a^2+(a-d)^2=(a+d)^2$
$\Rightarrow \quad a=4 d$
$\Rightarrow \quad \text { sides are } 3 d, 4 d, 5 d$
$\text { As area is } 24$
$\Rightarrow \quad \frac{1}{2} \times 3 d \times 4 d=24$
$\Rightarrow \quad d=2$
$\Rightarrow \quad \text { sides are } 6,8,10$
$\Rightarrow \quad \text { smallest side is } 6.$
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$(S 1)$ : If $\operatorname{Re}(A), \operatorname{Im}(A) > 0$, then the set $A$ contains all the real numbers
$(S2)$: If $\operatorname{Re}(A), \operatorname{Im}(A) < 0$, then the set $B$ contains all the real numbers,
Statement $2:$ Every tangent to the parabola, $y^2 = -4x$ will meet its axis at a point whose abscissa is non-negative.