Question

An umbrealla is made by stecking 10 t
pecies of
clothes of

two different colours each prices measuring 20cm, 50cm, and 50cm. how much clothe of each is required for the umbrella ​

Answer 1

Correct Question:-

An umbrella is made by stitching 10 triangular pieces of cloth of two different designs, each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each design is required for each colour?

Required Answer:-

GiveN:

• The sides of triangular pieces are 20 cm, 50 cm and 50 cm.

We need to find the area of triangle pieces of different colours. If there are 10 colours, then 5-5 pieces of each colour.

Then,

Semi-perimeter, s = Perimeter of ∆/2

= (20 + 50 + 50)/2 cm

= 120/2 cm

= 60 cm

Now using heron's formula:

Area of triangle = √{s(s - a)(s - b)(s - c)}

= √{60(60 - 20) (60 - 50) (60 - 50)}

= √{60 x 40 x 10 x 10} cm²

= 200√6 cm²

And,

• Cloth of each design required for one umbrella = Area of 5 triangular pieces

That is,

= 5 x 200√6

= 1000√6 cm²

Hence, 1000√6 cm² cloth of each colour are required for the umbrella$.$

Answer 2

Question:-

• An umbrella is made by stitching 10 triangular pieces of cloth of two different designs , each piece measuring 20 cm , 50 cm and 50 cm . How much cloth of each design of required for each colour.

To Find:-

• How much cloth of each design of required for each colour.

Given:-

• An umbrella is made by stitching 10 triangular pieces of cloth of two different designs , each piece measuring 20 cm , 50 cm and 50 cm.

Solution:-

Here ,

Semi-perimeter = Perimeter of ∆/2

$\tt\implies \: \dfrac { 20 + 50 + 50 } { 2 }$

$\tt\implies \: \cancel\dfrac { 120 } { 2 }$

$\tt\implies \: 60 \: cm$

Now ,

By using Herons Formula:-

$\tt\implies \: Area = \sqrt { s( s - a )( s - b )( s - c ) }$

$\tt\implies \: Area = \sqrt { 60( 60 - 20 ) ( 60 - 50 ) ( 60 - 50 ) }$

$\tt\implies \: Area = \sqrt { 60 \times 40 \times 10 \times 10 }$

$\tt\implies \: Area = 200\sqrt { 6 } { cm }^{ 2 }$

Then ,

Cloth of each design required:-

$\tt\implies \: 5 \times 200\sqrt { 6 }$

$\tt\implies \: 1000\sqrt { 6 } {cm}^{ 2 }$

Hence ,

• Required is 1000√6