GATE ME 2016 Set 2 — Question 5
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General Aptitude → Quantitative Aptitude → Mensuration & Geometry
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Question
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 is __________.
Correct answer
(B) 2.06
Solution
Let the side of the square be . Since the base of the equilateral triangle coincides with the side of the square, the side of the triangle is also .
The perimeter of the window consists of three sides of the square and two sides of the triangle (the shared side is internal).
Perimeter
Given perimeter , so .The area of the window is the sum of the area of the square and the area of the equilateral triangle:
Area
Area
Area .
Rounding to two decimal places, we get 2.06.
The perimeter of the window consists of three sides of the square and two sides of the triangle (the shared side is internal).
Perimeter
Given perimeter , so .The area of the window is the sum of the area of the square and the area of the equilateral triangle:
Area
Area
Area .
Rounding to two decimal places, we get 2.06.
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