Question

Both triangles are similar. The area of the smaller triangle is about 97 ft^sqrt. Which is the best approximation for the area of the larger triangle?
smaller triangle side: 12ft
bigger triangle side: 21ft

Answer 1

Could any of you give me an equation so i can solve the problem on my own?

Answer 2

Do you know the type of triangle..?

Answer 3

Equilateral sides.

Answer 4

Oh! Okay

Answer 5

The type of triangle is not significant.

Linear Measure Proportion a:b
Area Proportion: a^2:b^2

We know the similar triangle sides have the proportion 12:21 ==> 4:7
Thus, the area of the similar triangles must have the proportion 4^2:7^2 ==> 16:49

That's about it. How do we get 97 ft^2 in there?

Answer 6

Here's a picture of the shapes.

Answer 7

Knowing the type of triangle lets me use an easy equation.. Sorry?

Answer 8

It's okay, just do whatever it takes you need to do! :)

Answer 9

double check the side of the smaller and use that for the final calculation 12 vs 15

Answer 10

area of similar triangles is in ratio of sides as explained by @tkhunny above
the area of the smaller triangle is 97 so the area of the larger is 97 * (factor)
where factor is the inverse ratio of the lengths used.
if 15:21 then 97 * 7/5
if 12:21 then 3*4/3*7 then it would be 97 *7/4

Answer 11

Not Quite...

Length Ratio 4:7
Area Ratio 16:49

\(\dfrac{Smaller\;Area}{Larger\;Area} = \dfrac{16}{49}\)

\(\dfrac{97\;ft^{2}}{Larger\;Area} = \dfrac{16}{49}\)

\(Larger\;Area = 97\;ft^2\cdot\dfrac{49}{16}\)