Question

The area of a trapezium is 384 cm². Its parallel sides are in the ratio 3 : 5 and the perpendicular distance between them is 12 cm. Find the length of each one of the parallel sides.

Answer 1

Given:
Area of the trapezium = 384 cm² 
The parallel sides are in the ratio 3:5 and the perpendicular height between them is 12 cm.
Suppose that the sides are in x multiples of each other.
Then, length of the shorter side = 3x
Length of the longer side = 5x
Area of a trapezium \[=\frac{1}{2}\times(\text{ Sum of parallel sides })\times(\text{ Height })\]
\[ \Rightarrow 384 = \frac{1}{2} \times (3x+5x)\times(12)\]
\[ \Rightarrow 384=\frac{12}{2}\times(8x)\]
\[ \Rightarrow 384=6\times(8x)\]
\[ \Rightarrow 8x = \frac{384}{6}=64\]
\[ \Rightarrow x=\frac{64}{8}=8 cm\]
\[ \therefore\text{ Length of the shorter side }=3\times x=3\times 8=24 cm\]
\[\text{ And, length of the longer side }=5\times x=5\times 8 =40 cm\]