Triangle A has an area of #25 # and two sides of lengths #9 # and #6 #. Triangle B is similar to triangle A and has a side of length #8 #. What are the maximum and minimum possible areas of triangle B?

Answer 1

Area ob B could be 19.75 or 44.44

The areas of similar figures are in the same ratio as the ratio of the squares of the sides. In this case we do not know whether triangle b is bigger or smaller than triangle A, so we will have to consider both possibilities.

If A is bigger:# " " 9^2/8^2 = 25/x " "rArr x = (8^2 xx 25)/9^2#

Area = #19.75#

If A is smaller:# " " 6^2/8^2 = 25/x " "rArr x = (8^2 xx 25)/6^2#

Area = #44.44#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.