#### Question

The area of a trapezium is 384 cm^{2}. 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.

#### Solution

Given:

Area of the trapezium = 384 cm

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 \[=\frac{1}{2}\times(\text{ Sum of parallel sides })\times(\text{ Height })\]

\[ \Rightarrow 384 = \frac{1}{2} \times (3x+5x)\times(12)\]

\[ \Rightarrow 384=\frac{12}{2}\times(8x)\]

\[ \Rightarrow 384=6\times(8x)\]

\[ \Rightarrow 8x = \frac{384}{6}=64\]

\[ \Rightarrow x=\frac{64}{8}=8 cm\]

\[ \therefore\text{ Length of the shorter side }=3\times x=3\times 8=24 cm\]

\[\text{ And, length of the longer side }=5\times x=5\times 8 =40 cm\]

Area of the trapezium = 384 cm

^{2}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 \[=\frac{1}{2}\times(\text{ Sum of parallel sides })\times(\text{ Height })\]

\[ \Rightarrow 384 = \frac{1}{2} \times (3x+5x)\times(12)\]

\[ \Rightarrow 384=\frac{12}{2}\times(8x)\]

\[ \Rightarrow 384=6\times(8x)\]

\[ \Rightarrow 8x = \frac{384}{6}=64\]

\[ \Rightarrow x=\frac{64}{8}=8 cm\]

\[ \therefore\text{ Length of the shorter side }=3\times x=3\times 8=24 cm\]

\[\text{ And, length of the longer side }=5\times x=5\times 8 =40 cm\]

Is there an error in this question or solution?

Solution 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. Concept: Area of Trapezium.