Triangle A has an area of $3$ $3$ and two sides of lengths $3$ $3$ and $6$ $6$ . Triangle B is similar to triangle A and has a side with a length of $11$ $11$ . What are the maximum and minimum possible areas of triangle B?

Question

Triangle A has an area of $3$ $3$ and two sides of lengths $3$ $3$ and $6$ $6$ . Triangle B is similar to triangle A and has a side with a length of $11$ $11$ . What are the maximum and minimum possible areas of triangle B?

1 Answer

Impact of this question

1652 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-17T02:01:07

The triangle inequality states that the sum of any two sides of a triangle MUST be greater than the 3rd side. That implies the missing side of triangle A must be greater than 3!

Explanation:

Using the triangle inequality ...

$x + 3 > 6$ $x+3>6$
$x > 3$ $x>3$

So, the missing side of triangle A must fall between 3 and 6.

This means 3 is the shortest side and 6 is the longest side of triangle A.

Since area is proportional to the square of the ratio of the similar sides ...

minimum area $= {(\frac{11}{6})}^{2} \times 3 = \frac{121}{12} \approx 10.1$ $= (11/6)^2xx3=121/12~~10.1$

maximum area $= {(\frac{11}{3})}^{2} \times 3 = \frac{121}{3} \approx 40.3$ $=(11/3)^2xx3=121/3~~40.3$

Hope that helped

P.S. - If you really want to know the length of the missing 3rd side of triangle A, you can use Heron's area formula and determine that the length is $\approx 3.325$ $~~3.325$ . I'll leave that proof to you :)

Science

Math

Humanities

... and beyond

Triangle A has an area of $3$ $3$ and two sides of lengths $3$ $3$ and $6$ $6$ . Triangle B is similar to triangle A and has a side with a length of $11$ $11$ . What are the maximum and minimum possible areas of triangle B?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

Triangle A has an area of 33 and two sides of lengths 33 and 66 . Triangle B is similar to triangle A and has a side with a length of 1111 . What are the maximum and minimum possible areas of triangle B?

1 Answer

Explanation:

Related questions

Impact of this question

Triangle A has an area of $3$ $3$ and two sides of lengths $3$ $3$ and $6$ $6$ . Triangle B is similar to triangle A and has a side with a length of $11$ $11$ . What are the maximum and minimum possible areas of triangle B?