Question

Subject: Mathematics
Scenario: For the decoration on Divya's birthday, Keerthana and Megha prepared coloured paper penants in the form of triangles in three sizes.
- Blue coloured penants of sides 3 inches, 4 inches, 5 inches.
• Yellow coloured penants of sides 8 inches, 5inches, Sinches.
- Red coloured penants of sides 5inches, 7inches, 8 inches They prepared 40 penants of each colour.
Question: If each coloured paper sheet is available in 24inches x24 inches, what is the minimum number of sheets required of each colour?

A) 1blue, 1yellow,1red
B)1blue, 2yellow, 3red
C) 2 blue, 1yellow,2 red
D) 1blue.1yellow, 2red​

Answer 1

Answer:

Answer is :- Option 'D' 1blue,1yellow,2red.

Step-by-step explanation:

576 sq Inches (area of sheet) ÷ 6 inches (area of one blue penant) = 96 penants.

576 sq Inches (area of sheet) ÷ 12 inches (area of one yellow penant) = 48 penants.

576 sq Inches (area of sheet) ÷ 17.32 inches (area of one red penant) = 33 penants.

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.Hope my answer is helpful for you. Good Luck

Answer 2

Solution :-

Blue coloured penants of sides 3 inches, 4 inches, 5 inches :-

→ 3² + 4² = 5²

so, triangle formed is a right angled ∆ .

then,

→ Area of 40 penants of blue colour = 40 * (1/2) * 3 * 4 = 240 inches² .

therefore, to cover 240 inches² area only 1 paper sheet of blue colour of size 24 * 24(576 inches²) is needed.

Yellow coloured penants of sides 8 inches, 5inches, 5 inches :-

→ semi perimeter = 8 + 5 + 5 / 2 = 9 = s

so,

→ Area of each ∆ = √[s * (s - a) * (s - b) * (s - c)] = √[9 * (9 - 8) * (9 - 5) * (9 - 5)] = √(9 * 4 * 4) = 12 inches².

then,

→ Area of 40 penants of yellow colour = 40 * 12 = 480 inches² .

therefore, to cover 480 inches² area only 1 paper sheet of yellow colour of size 24 * 24(576 inches²) is needed.

Red coloured penants of sides 5 inches, 7 inches, 8 inches :-

→ semi perimeter = 5 + 7 + 8 / 2 = 10 = s

so,

→ Area of each ∆ = √[s * (s - a) * (s - b) * (s - c)] = √[10 * (10 - 8) * (10 - 5) * (10 - 7)] = √(10 * 5 * 3 * 2) = 17.32 inches².

then,

→ Area of 40 penants of yellow colour = 40 * 17.32 = 692.8 inches² .

therefore, to cover 692.8 inches² area 2 paper sheet of red colour of size 24 * 24(576 inches²) is needed.

hence, option D) 1 blue, 1yellow, 2red is correct answer .

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