Question

The area of a trapezium is 384 cm square it's parallel sides are in the ratio 5:3 and the distance between them is 12cm the longer side is

Answer 1

given :-

area of the trapezium = 384cm²

distance between the parallel sides (height) = 12cm

ratio between the parallel sides (bases) = 5 : 3

let the bases of the trapezium be 5x and 3x respectively.

formula to find the area of a trapezium is 1/2 × h(b1 + b2)

where b1 and b2 are the parallel sides and h is the distance between them.

➡ 1/2 × h(b1 + b2) = 384cm²

➡ 1/2 × 12(5x + 3x) = 384cm²

➡ 6(8x) = 384cm²

➡ 48x = 384cm²

➡ x = 384/48

➡ x = 8

hence,

• b1 = 5x = 5 × 8 = 40cm

• b2 = 3x = 3 × 8 = 24cm

Answer 2

hello there

Step-by-step explanation:

Question:The area of a trapezium is 384 cm square it's parallel sides are in the ratio 5:3 and the distance between them is 12cm the longer side is?

To find : Length of Longer side ?

Answer:

Given:

Height of th Trapezium = 12 cm

Area of the Trapezium =384cm×cm

--> Now, we To find the Length we have to select a common multiple say x

So, The b, a be the side of trapezium in the ratio 5 : 3

Therefore ,

a = 3x

b = 5x

Also , we know that :

■ Area of Trapezium = (1/2)× (sum of parallel sides) × h

--> [ Where h is the height of the Trapezium ]

Now , putting the values in the formulae respectively

■ 384 = (1/2)× (3x +5x) × 12

■ 384 = (1/2)× ( 8x ) ×12

■ 384 = 8x × 6

■ 8x = 384/6

■ 8x = 64

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■ ■ x = 8 cm ■ ■

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Now , puting the value of x in the respective sides of the Trapezium

therefore:

a = 3x = 3×8 =24 cm

b = 5x = 5×8 =40 cm

So, the longer side of the Trapezium is b.

■ Longer side = b = 40 cm

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Hope it helps

Thank you!