Puzzle-35. Find the Length DE. ABCD is rectangular. 5 areas are same sizes. AB=13 cm.

[ttokoro]

Not a question of mathcad but Mathcad can solve this.

Find the Length DE.

ABCD is rectangular. 5 areas are same sizes. AB=13 cm.

[Werner_E]

Its not difficult to get DE=6, but Mathcad or Prime were of no help here (or rather: weren't needed).

[terryhendicott · Accepted solution]

Hi

See Enclosed

[Werner_E]

To be on the safe side we would need a symbolical solution, but trying to evaluate  the solve block symbolically fails.

Reason is that yD actually is irrelevant and yD could be set to any constant value and need not to be solved for.

So when we solve for four unknowns, we also only need four equations - one of the area equations is redundant anyway - if four of the five trinagles have an area of 1/5 of the total area, I would be surprised if the fifth triangle would have another area.
Now symbolical evaluation works OK

[Fred_Kohlhepp]

Attached. prime 4 express

[ttokoro]

Hights of triangle DEG and ECH are not same but areas are same.

[Werner_E]

Sorry, can't follow your logic 😞

Actually DE=6 cm, not 6.5 cm. E is not halving DC.

[Fred_Kohlhepp]

I stand corrected.  Trying to explain my logic revealed my error.

[Werner_E]

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Trying to explain my logic revealed my error.

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I know exactly what you are talking about -  I know that situation all too well myself! 😉