UPSC 2017 CDS II Math Paper

Let the side of the square be x units and the length of equal sides of the isosceles triangle be y units.
∴3x+2y=

7

6

×4x
⇒2y=

14

3

x−3x=

5x

3

⇒y=

5x

6

EF ⊥ CD
∴DF=CF=

x

2

Remember: In an isosceles triangle, the perpendicular from the vertex to the base bisects the base.
In right ΔDEF
EF=√y2−(

x

2

)2

Area of triangle‌

‌Area of square‌

=

1 2 ×CD×EF

CD2

=

1 2 × 2x 3

x

=

1

3

Thus, the ratio of area of the triangle to the area of the original square is 1 : 3.