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Elementary schoole children can solve this puzzle. If you need you can use Mathcad Prime.
Solved! Go to Solution.
There are two intermediate solutions. In the end AB=11 in any case 😉
If we use Mathcad it is easy to find the answer. But without sqrt or functions, this puzzle becomes very hard.
This task is not particularly difficult. Students should be able to solve it using the cosine law for side length and the sine formula for the area of a triangle. What is much more interesting about this problem is that solution "11" is possible in two different geometric situations.
The two solutions are AD=14.354..., BC=11.822... and AD=5.911..., BC=28.709...
They are approximations for unpleasant radicals.
BTW.
Numerical solutions attached. How do you solve the system symbolically? Need help.
My answer is.
Additional task: 😉
Given pieces and requirements as usual.
But:
Instead of the given area F=60, the distance AC must now be calculated so that the area of the triangle ABC is maximum. How big is the interior angle at C?
Correction:
With the unusual names of the triangle vertices as shown in the sketch in the original problem, the distance AB is logically sought. I accidentally had the usual point designation in my head, where A and B limit the lower side of the triangle and C is the summit.
I would solve it that way:
Using Mathcads solving and plotting facilities it may look like this:
Mathcad 15 sheet attached