Question

Prove that the ratios of the areas of two similar triangles is equal to the ratio of the squares of the corresponding sides by using equilateral triangles scelane triangles

Answer 1

We can prove this by formulating a theorm like the given statement such as 

If ΔABC ~ ΔDEF such that BC = 3 cm and EF = 4 cm and the 
area of ΔABC = 54 cm 2 . Find the area of ΔDEF.

As given in the statement we get, 

Area of ΔABC/ Area of ΔDEF  =  BC²/ EF²
Putting the values 
54/ Area of ΔDEF = 32/ 42
or
Area of DEF = 54 x 16/ 9
Area of DEF = 96 cm²