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?

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Answer 1 · 2018-02-18T05:33:39

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

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

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#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#