An isosceles triangle is drawn outside on one of the sides of a square as base in such a way that th...........

Quantitative Aptitude (CDS) Mensuration 2D

An isosceles triangle is drawn outside on 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 original square. What is the ratio of area of the triangle to the area of the original square?

1 : 1

2 : 3

1 : 2

1 : 3

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Explanation:

Let the side of each of the square be a and the other two sides of the triangle be x
Given, Perimeter of the complete figure = 7/6(perimeter of the original square)
=>3a + 2x = 7/6(4a) =>3a + 2x = 7/3(2a)
=>3(3a + 2x) = 14a
=>9a + 6x = 14a
=>6x = 5a ………(i)
Using Pythagoras theorem
In upper triangle:

Again,
Ratio of the area of triangle to the original square =
Hence required ratio be 1 : 3