Question

The parallel sides of a trapezium are in the ratio 4 : 7 and the distance between them is 10 m. If the area of the

trapezium is 220 m2

, find the lengths of the parallel sides.​

Answer 1

Answer:

17.6 m, 30.8m

Step-by-step explanation:

Let the length of the parallel sides be 4x metre and 7x metre.

Height = 10 m

Area = 220 m^2

We know that formula for the area of a trapezium is

1/2 (sum of parallel sides) × Height

So,

1/2 (7x + 3x) × 10 = 220

or, 10x × 5 = 220

or, x = 220/50

or, x = 4.4

So, lengths are 4.4 × 4 m = 17.6 m

4.4 × 7 m = 30.8 m

Answer 2

• Length of one parallel side = 16 m.
• Length of other parallel side = 28 m.

Given :–

• The parallel sides of a trapezium are in the ratio = 4 : 7.
• The distance between both parallel sides = 10 m.
• Area of the trapezium = 220 m².

To Find :–

• The length of both parallel sides.

Solution :–

Let,

The one parallel side be 4x.

The other parallel side be 7x.

First, we need to find the value of x.

Area of the trapezium,

$\mapsto \red{\sf \dfrac{1}{2} \times (Sum \: of \: both \: parallel \: sides) \times h}$

Given that,

Distance between both parallel sides = height = 10 m.

Area of the trapezium = 220 m²

$\hookrightarrow \dfrac{1}{ \cancel2} \times (4x + 7x ) \times \cancel{10} \: m = 22 0 \: {m}^{2}$

$\hookrightarrow1 \times 11x \times 5 \: m = 220 \: {m}^{2}$

$\hookrightarrow11x = \cancel\dfrac{220 \: {m}^{2} }{ 5 \: m}$

$\hookrightarrow11x = 44 \: m$

$\hookrightarrow x = \cancel\dfrac{44}{11} \: m$

$\hookrightarrow x = 4 \: m$

Now, we have to find the length of both parallel sides.

One parallel side = 4x = 4 × 4 m = 16 m

Other parallel side = 7x = 7 × 4 m = 28 m

Hence,

The length of both parallel sides are 16 m and 28 m.

Verification :–

Area of the trapezium,

$\mapsto \red{\sf \dfrac{1}{2} \times (Sum \: of \: both \: parallel \: sides) \times h}$

Values are,

• Area of the trapezium = 220 m².
• Height = 10 m.
• Length of one parallel side = 16 m.
• Length of other parallel side = 28 m.

Now, substitute all the values in the formula of area of the trapezium.

$\hookrightarrow \dfrac{1}{ \cancel2} \times (16 \: m + 28 \: m) \times \cancel{10} \: m = 220 \: {m}^{2}$

$\hookrightarrow1 \times 44 \: m \times 5 \: m = 220 \: {m}^{2}$

$\hookrightarrow220 \: {m}^{2} = 220 \: {m}^{2}$

Hence Verified !