Question

Prove that
ariea of equilateral talangle LSM]
described
area of
on one side of square is equal to half ]
grilateral triangle described on one of its diognals​

Answer 1

Step-by-step explanation:

R.E.F.Image

Let ABCD be a square of side a.

Therefore diagonal =

2

a

Two equilateral triangles are

ABE , DBF

Length of one side of

ΔABE=a

ΔDBF=

2

a

We know equilateral triangle have all angles as 60

∘

; so all equilateral triangles are similar to other.

∴

areaofΔDEF

areaofΔABE

=(

2a

a

)

2

=

2

1

∴ proved.