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A window is made up of a square portion and an equilateral triangle portion above it. The base of
the triangular portion coincides with the upper side of the square. If the perimeter of the window
is 6 m, the area of the window in m2 is
  • a)
    1.43
  • b)
    2.06
  • c)
    2.68
  • d)
    2.88
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A window is made up of a square portion and an equilateral triangle po...
Area of the window = Area of square + Area of equilateral triangle = 1
[Perimeter of the window is 6 m
⇒ 4x+2x = 6, where x is length of each side]
⇒ x = 1
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A window is made up of a square portion and an equilateral triangle po...
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A window is made up of a square portion and an equilateral triangle po...
To solve this problem, we need to find the area of the window given its perimeter.

Let's assume that the side length of the square portion is 'x' and the side length of the equilateral triangle portion is 'y'.

The perimeter of the window is given as 6 m, so we can write the equation as:

4x + 3y = 6

Since the base of the triangular portion coincides with the upper side of the square, the side length of the equilateral triangle is equal to the side length of the square. Therefore, we can write y = x.

Now, substitute y = x into the equation:

4x + 3x = 6
7x = 6
x = 6/7

Now, we can find the side length of the square (x) and the side length of the equilateral triangle (y).

x = 6/7 m
y = 6/7 m

To find the area of the window, we need to calculate the area of the square and the area of the equilateral triangle and then add them together.

Area of the square = side length * side length = x * x = (6/7) * (6/7) = 36/49 m^2

Area of the equilateral triangle = (sqrt(3) / 4) * side length^2 = (sqrt(3) / 4) * (6/7)^2 = (sqrt(3) / 4) * (36/49) = 18sqrt(3) / 49 m^2

Total area of the window = Area of the square + Area of the equilateral triangle = 36/49 + 18sqrt(3) / 49 = (36 + 18sqrt(3)) / 49 ≈ 1.43 m^2

Therefore, the correct answer is option A) 1.43 m^2.
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A window is made up of a square portion and an equilateral triangle portion above it. The base ofthe triangular portion coincides with the upper side of the square. If the perimeter of the windowis 6 m, the area of the window in m2 isa)1.43b)2.06c)2.68d)2.88Correct answer is option 'A'. Can you explain this answer?
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A window is made up of a square portion and an equilateral triangle portion above it. The base ofthe triangular portion coincides with the upper side of the square. If the perimeter of the windowis 6 m, the area of the window in m2 isa)1.43b)2.06c)2.68d)2.88Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A window is made up of a square portion and an equilateral triangle portion above it. The base ofthe triangular portion coincides with the upper side of the square. If the perimeter of the windowis 6 m, the area of the window in m2 isa)1.43b)2.06c)2.68d)2.88Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A window is made up of a square portion and an equilateral triangle portion above it. The base ofthe triangular portion coincides with the upper side of the square. If the perimeter of the windowis 6 m, the area of the window in m2 isa)1.43b)2.06c)2.68d)2.88Correct answer is option 'A'. Can you explain this answer?.
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