GATE2016 ME-2: GA-5

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 $m^{2}$ is ___________.

• A. $1.43$
• B. $2.06$
• C. $2.68$
• D. $2.88$

Answer 1

Perimeter(window) $= 6$ m

$\implies 5a = 6$ m

$\implies a = \dfrac{6}{5}$ m

$\implies a = 1.2$ m

Area(window) $=$ Area(triangle) $+$ Area(square)

 $\qquad = \dfrac{\sqrt{3}}{4}a^2 + a^2$

 $\qquad = \dfrac{\sqrt{3}}{4}{(1.2)}^2 + {(1.2)}^2$

 $\qquad = 2.06 \ \text{m}^2$

Correct Answer: $B$

Answer 2

Perimeter is $6$ so side length is $\dfrac{6}{5} = 1.2 m$

So area of square is $1.2\times 1.2 = 1.44$

Area of equilateral triangle $=\dfrac{\sqrt{3}}{4} \times 1.2\times 1.2 = 0.62352$

So, total area is $0.62352 + 1.44 =2.06352$ so answer is $B$

Comments

Why 6/5 bro? Can you elaborate?

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let side = a then perimeter = 5*a

now 5*a = 6 (given)

so side length = 6/5