Triangle A has an area of #60 # and two sides of lengths #12 # and #15 #. Triangle B is similar to triangle A and has a side of length #5 #. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum area 10.4167 and Minimum area 6.6667

#Delta s A and B # are similar.
To get the maximum area of #Delta B#, side 5 of #Delta B# should correspond to side 12 of #Delta A#.
Sides are in the ratio 5 : 12 Hence the areas will be in the ratio of #5^2 : 12^2 = 25 : 144#
Maximum Area of triangle #B =( 60 * 25) / 144= 10.4167#
Similarly to get the minimum area, side 15 of #Delta A # will correspond to side 5 of #Delta B#. Sides are in the ratio # 5 : 15# and areas #25 : 225#
Minimum area of #Delta B = (60*25)/225= 6.6667#
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Answer 2

The maximum and minimum possible areas of Triangle B can be calculated based on the ratio of the corresponding sides of Triangle B to Triangle A.

Given that Triangle B is similar to Triangle A, the ratio of corresponding sides is constant.

Let's denote the ratio of corresponding sides of Triangle B to Triangle A as ( k ).

The ratio of corresponding sides of Triangle B to Triangle A is given by: [ k = \frac{5}{15} = \frac{1}{3} ]

Therefore, the ratio ( k ) is ( \frac{1}{3} ).

Now, to find the maximum and minimum possible areas of Triangle B:

  1. Maximum Area: [ \text{Max Area of B} = (\text{Max Area of A}) \times k^2 ] [ \text{Max Area of B} = (60) \times \left(\frac{1}{3}\right)^2 ] [ \text{Max Area of B} = 60 \times \frac{1}{9} ] [ \text{Max Area of B} = 6.67 ]

  2. Minimum Area: [ \text{Min Area of B} = (\text{Min Area of A}) \times k^2 ] [ \text{Min Area of B} = (60) \times \left(\frac{1}{3}\right)^2 ] [ \text{Min Area of B} = 60 \times \frac{1}{9} ] [ \text{Min Area of B} = 6.67 ]

Therefore, the maximum possible area of Triangle B is ( 6.67 ) square units and the minimum possible area is also ( 6.67 ) square units.

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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.

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.

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.

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.

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