Question

Kevin asks his friend Neev to draw an equilateral triangle on the base of the rectangle (Length as base) and another equilateral triangle with diagonal of a rectangle as a base. He also asked him to find the ratio of the area of a triangle with diagonal as base to area of a triangle with length as a base. Explain and prove this situation mathematically.​

Answer 1

Explanation:

Area of square =a

2

Length of the diagonal =

2a

Area of equilateral triangle with side

2a

=

4

3

×(

2a

)

2

=

2

3

a

2

then,

Required ratio =

a

2

3

a

2

/2

=

2

3

Hence, ratio is

3

:2