Question

Triangle A has an area of `4` and two sides of lengths `9` and `3`. Triangle B is similar to triangle A and has a side with a length of `32`. What are the maximum and minimum possible areas of triangle B?

Answer 1

`A_(Bmax) = color(green)( 110.0779`

`A_(Bmin) = color(red)(28.9245`

Explanation:

#Given : Delta A (PQR) p = 9, q = 3, A_A = 4, z = 32

To find `A_(Braxton), A_(Bmin)`

Let x,y,z be the sides of second `Delta B`

`r < (9+3), > (9-3)` as sum of the two sides greater than the third side.

Hence, `r= 6.1.`, for maximum area of `Delta B` and `r_(min)= 11.9` for minimum area of `Delta B`, r being rounded for one decimal.

We know, `p / x = q / y, r / z` since the two triangles are similar.

Then he areas will be proportional to the square of the sides.

`:. A_B = A_A * (z/r)^2`

`A_(Bmax) = 4 * (32/6.1)^2 =color(green)( 110.0779`

`A_(Bmin) = 4 * (32/11.9)^2 = color(red)(28.9245`