SOLUTION: An isoceles triangle whose are is 1200 square meters and height 40m is cut parallel to its non-congruent side producing a trapezoid and a triangle whose areas are equal. Find the h

Question 1012945: An isoceles triangle whose are is 1200 square meters and height 40m is cut parallel to its non-congruent side producing a trapezoid and a triangle whose areas are equal. Find the height of the new triangle and the height of the trapezoid.
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
The triangle before making the cut:
Altitude 40, unknown base b, area 1200.

Same or congruent triangle, now draw a segment through the altitude, this segment parallel to the b=60 base. The upper region is another isosceles triangle with altitude h and base x. The lower region is trapezoid with altitude a and TWO bases are x and 60.
-

That is according to the description of the two regions being of equal areas, and the two heights being the original given triangle height (altitudes).
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Note this is a system of three equations in three unknown variables.

Use first equation as h=40-a, and substitute into the other two equations,

and observing that both of these have a term, ;

SUBSTITUTE into ...

doing the steps,
..
..
---height for the trapezoid.

Still want to find h and for this, return to .
.--------height for the triangle.
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