Question:
Mark (✓) against the correct answer:
The area of a trapezium is 384 cm2. Its parallel sides are in the ratio 5 : 3 and the distance between them is 12 cm. The longer of the parallel sides is
(a) 24 cm
(b) 40 cm
(c) 32 cm
(d) 36 cm
Solution:
(b) $40 \mathrm{~cm}$
Let the length of the parallel sides be $5 x \mathrm{~cm}$ and $3 x \mathrm{~cm}$, respectively.
$^{2}$ $A$ rea of the trapezium $=\left\{\frac{1}{2} \times(5 x+3 x) \times 12\right\} \mathrm{cm}$
$=\left(\frac{1}{2} \times 8 x \times 12\right) \mathrm{cm}^{2}=48 \times \mathrm{cm}^{2}$
But, the area of the trapezium is $384 \mathrm{~cm}^{2}$.
$48 x=384$
$\Rightarrow x=\frac{384}{48}=8$
$L$ onger side $=5 \mathrm{x}=5 \times 8=40 \mathrm{~cm}$