a smaller triangle is having three sides. another big triangle is having sides exactly double the sides of the smaller triangle. then what is the ratio of area of smaller triangle to area of the bigger triangle?
The ratio of the area of the smaller triangle to the bigger triangle is 1 : 4.
Why this happens (quick idea)
If every side of a triangle is doubled, all its linear dimensions (including height) are doubled. The area of a triangle depends on the product of two lengths (like base and height), so when each length is doubled, the area becomes 2×2=42\times 2=42×2=4 times larger.
So:
- Area of smaller triangle = AAA
- Area of bigger triangle = 4A4A4A
Therefore,
Area(small) : Area(big) = 1 : 4.
TL;DR: When the sides are doubled, the area becomes four times, so the required ratio is 1:4.
