Question

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

Answer 1

Given :-

Sides of two similar triangles are in the ratio of 4:9

To Find :-

Ratio of their area

Solution :-

Area of ΔABC ∼ ΔPQR

ΔABC/ΔPQR = (side)²/side²

ΔABC/ΔPQR = (4)²/(9)²

ΔABC/ΔPQR = 16/81

Hence

The ratio is 16 : 81

Answer 2

Answer:

• 16 : 81.

Step-by-step explanation:

Since, the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

• ΔABC ~ΔDEF

⟹ ar(ΔABC)/ar(ΔDEF) = BC²/EF²

⇒ ar(ΔABC)/ar(ΔDEF) = 4²/9²

• 16/81

∴ Areas of these two triangles are in the ratio 16 : 81.

We also have,

⟹ ar(ΔABC)/ar(ΔDEF) = AB²/DE² = CA²/DF²