The lengths of the parallel sides of a trapezium are in the ratio $5 : 3$ and the distance between them is $12.5 c m$ . If the area of the trapezium is $450 c m^{2}$ , find the lengths of its parallel sides.

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Solution

Length of parallel sides are in ratio $5 : 3$ Let the larger side $= 5 x$
$\Rightarrow$ Smaller side $= 3 x$
$h = 12.5 c m$
Area $= \frac{1}{2}$ (Sum of parallel sides) $\times$ (height)
$\Rightarrow 450 = \frac{1}{2} (5 x + 3 x) (12.5)$
$450 = \frac{1}{2} (8 x) (12.5) = 50 x$
$\Rightarrow x = \frac{1150}{50} = 9$
$\Rightarrow$ length of larger side $= 5 x = 45 c m$
Smaller side $= 3 x = 27 c m$

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The lengths of the parallel sides of a trapezium are in the ratio 5:3 and the distance between them is 12.5 cm. If the area of the trapezium is 450 cm2, find the lengths of its parallel sides.

Length of parallel sides are in ratio 5:3 Let the larger side =5x⇒ Smaller side =3xh=12.5 cmArea =12 (Sum of parallel sides)× (height)⇒450=12(5x+3x)(12.5)450=12(8x)(12.5)=50x⇒x=115050=9⇒ length of larger side =5x=45 cmSmaller side =3x=27 cm

The lengths of the parallel sides of a trapezium are in the ratio $5 : 3$ and the distance between them is $12.5 c m$ . If the area of the trapezium is $450 c m^{2}$ , find the lengths of its parallel sides.