26
Find length and breadth of a rectangular park whose perimeter is $100 \text{ m}$ and area is $600 \text{ m}^2$.
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Let length and breadth of the park be $a$ metres and $b$ metres respectively.
$2(a + b) = 100 \dots(i)$ ($\frac{1}{2}$ mark)
$ab = 600 \dots(ii)$ ($\frac{1}{2}$ mark)
using (i) & (ii) we get $a^2 - 50a + 600 = 0$ (1 mark)
$\Rightarrow a = 30 \text{ or } 20$ ($\frac{1}{2}$ mark)
and $b = 20 \text{ or } 30$ ($\frac{1}{2}$ mark)
$\therefore \text{length} = 30 \text{ m, breadth} = 20 \text{ m or vice versa}$
$2(a + b) = 100 \dots(i)$ ($\frac{1}{2}$ mark)
$ab = 600 \dots(ii)$ ($\frac{1}{2}$ mark)
using (i) & (ii) we get $a^2 - 50a + 600 = 0$ (1 mark)
$\Rightarrow a = 30 \text{ or } 20$ ($\frac{1}{2}$ mark)
and $b = 20 \text{ or } 30$ ($\frac{1}{2}$ mark)
$\therefore \text{length} = 30 \text{ m, breadth} = 20 \text{ m or vice versa}$