The parallel sides of an isosceles trapezium are in the ratio $2 : 3$ . If its height is $8 c m$ and area is $240 c m^{2}$ , then its perimeter is ____ cm.

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Solution

The correct option is D
80

Let the parallel sides AB and DC be $2 x$ and $3 x$ respectively.

Area = $\frac{1}{2} (2 x + 3 x) h$

$240 = \frac{1}{2} (5 x) \times 8$

$x = 12$

$∴ A B = 2 (12) = 24 c m$

$D C = 3 (12) = 36 c m$

We know $E C = \frac{36 - 24}{2} = \frac{12}{2} = 6 c m$

In $△ B E C, B C = 10 c m$ $(3 - 4 - 5 P y t h a g o r a s T r i p l e t)$

Hence perimeter of trapezium = $24 + 10 + 36 + 10$

$= 80 c m$

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The parallel sides of an isosceles trapezium are in the ratio 2:3. If its height is 8cm and area is 240cm2, then its perimeter is ____ cm.

The correct option is D 80 Let the parallel sides AB and DC be 2x and 3x respectively. Area = 12(2x+3x)h 240=12(5x)×8 x=12 ∴AB=2(12)=24cm DC=3(12)=36cm We know EC=36−242=122=6 cm In △BEC,BC=10cm (3−4−5PythagorasTriplet) Hence perimeter of trapezium = 24+10+36+10 =80cm

The parallel sides of an isosceles trapezium are in the ratio $2 : 3$ . If its height is $8 c m$ and area is $240 c m^{2}$ , then its perimeter is ____ cm.