Question

3. One of the parallel sides of a trapezium is double the other and its height is 24 cm. If area of
the trapezium is 360 cm?, find the length of the parallel sides.​

Answer 1

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

Answer 2

Answer:

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 :-

• length of parallel sides of trapezium

Solution :-

Let the 1st parallel side be x

Another parallel sides be 2x

360 = ½(2x + x) 24

360 = ½ × 24(2x + x)

360 = 1 × 12(3x)

360 = 12(3x)

360/12 = 3x

30 = 3x

30/3 = 10

Parallel sides are

1(10) = 10 cm

2(10) = 20 cm

Verification :-

360 = ½(a + b) h

360 = ½(10 + 20) 24

360 = ½ × 30 × 24

360 = 15 × 24

360 = 360

Hence, verified