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Question

An isosceles triangle is drawn outside of one of the sides of a square as base in such a way that the perimeter of the complete figure is 7/6 times the perimeter of the complete original square. What is the ratio of area of the triangle to the area of the original square?

This question was previously asked in
CDS I 2017 General Knowledge Previous Year Paper (05-Feb-2017)
The correct answer is

1 : 3

Let the square side be a and each equal triangle side be b. The outer perimeter is 3a + 2b = (7/6) × 4a, giving b = 5a/6. Triangle height = √[(5a/6)² − (a/2)²] = 2a/3. Its area is a²/3, while the square area is a². Thus the ratio is 1 : 3.

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