# 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. - Mathematics

Sum

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.

#### Solution

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 $=\frac{1}{2}\times(\text{ Sum of parallel sides })\times(\text{ Height })$
$\Rightarrow 384 = \frac{1}{2} \times (3x+5x)\times(12)$
$\Rightarrow 384=\frac{12}{2}\times(8x)$
$\Rightarrow 384=6\times(8x)$
$\Rightarrow 8x = \frac{384}{6}=64$
$\Rightarrow x=\frac{64}{8}=8 cm$
$\therefore\text{ Length of the shorter side }=3\times x=3\times 8=24 cm$
$\text{ And, length of the longer side }=5\times x=5\times 8 =40 cm$
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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 20 Mensuration - I (Area of a Trapezium and a Polygon)
Exercise 20.2 | Q 13 | Page 23