Question

The parallel sides of an isosceles trapezium are in the ratio 2 : 3. If its height is 4cm and area is 60 square cm.find the perimeter.​

Answer 1

Answer:

we know that

the parallel sides are in ratio 2:3

Let one side be 2x

Then the other side will be 3x.

Given,

height=4cm

We know that,

Ar(Trapezium)=1/2*(sum of parallel sides)*(height)

60=1/2*(2x+3x)*4

60=2*5x

x=6

therefore shorter parallel side is 12cm and longer side is 18cm.

Now longer side is longer than shorter side by 6cm.

Since it is isosceles, therefore the side protrudes equally on both side. Taking one half the longer side will be 3cm longer.

SEE THE ATTACHMENT ABOVE FOR DIAGRAM.

Using Pythagoras theorem,

(1 non parallel side)^2=height^2+ protuded part^2

1 non parallel side=√(4^2+3^2)

5cm.

Perimeter=sum of all sides

12+18+5+5

40cm

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