Question

one of the parallel sides of a trapezium is double the other and its height is 24cm. if area of the trapezium is 360 cm square,find the length of the parallel sides.​

Answer 1

Answer:

Let the lengths of the two parallel sides of the trapezium be X and 2 X cm respectively.

We know that

Area of the trapezium

=

2

1

(Sum of parallel sides) × (Distance between them)

∴180=

2

1

(x+2x)×12

or 180×2=3x×12

or 180×2=3x×12

or 36x=360

or x=10

∴ The sides of the trapezium are 10 cm and 20 cm respectively

Answer 2

Given :

One of the parallel sides of trapezium is double the other

Height of the trapezium = 24 cm

Area of trapezium = 360 cm²

To Find :

The length of parallel sides of trapezium

Solution :

Let length of one of the parallel sides be "x" then the length of the other side becomes "2x".

Area of trapezium is given by ,

$\\ \star{\boxed{\purple{\sf{Area = \frac{1}{2} \times (a + b) \times h }}}}$

here ,

a and b are lengths of parallel sides

h is height of trapezium

Subatituting the values we have in the formula ,

$\\ : \implies \sf \: 360 = \frac{1}{2} \times (x + 2x) \times 24$

$\\ : \implies \sf \: 360 = \frac{1}{2} \times 3 {x} \times 24$

$\\ : \implies \sf \: 3{x}^{} \times 12 = 360$

$\\ : \implies \sf \: {x}^{} = \frac{360}{36}$

$\\ : \implies{\underline{\boxed {\pink{\mathfrak{x =10 }}}}} \:\bigstar$

Now ,

Length of one of the parallel side (x) = 10 cm

Then ,

The length of the other parallel side (2x) = 2(10) = 20 cm

Hence ,

Lengths of the parallel sides of given trapezium are 10 cm and 20 cm