Question

SIDES OF TWO SIMILAR TRIANGLES ARE IN THE RATIO 4 : 9, AREAS OF THESE TRIANGLES ARE IN THE RATIO ?

Answer 1

Answer:

And the ratio of the sides of these two similar triangles be AB: PQ which is 4:9. If two triangles are similar, then the ratio of the areas of both the triangles is equal to the ratio of the squares of their corresponding sides. So, the correct answer is “16:81”.

Answer 2

Answer:

Let us assume that ABC and DEF are two similar triangles, such that,

ΔABC ~ ΔDEF

And AB/DE = AC/DF = BC/EF = 4/9

As, the ratio of the areas of these triangles will be equal to the square of the ratio of the corresponding sides,

∴ Area(ΔABC)/Area(ΔDEF) = AB2/DE2 

∴ Area(ΔABC)/Area(ΔDEF) = (4/9)2 = 16/81 = 16:81

Therefore, if the sides of two similar triangles are in the ratio 4: 9, then the areas of these triangles are in the ratio 16: 81.