Given a trapezoid with bases $437\mathrm{m}$ and $57\mathrm{m}$ with sides $300\mathrm{m}$ and $350\mathrm{m}$
, it is to be divided into two parts in the ratio $2:3$ by a line parallel to the parallel sides, the $\color{brown}{\text{larger part be adjacent to the smaller parallel side}}$. Find the length of the dividing line, the altitude of the trapezoid and the area of the trapezoid.
I managed to solve for the trapezoid's $\text{height}(296.012\mathrm{m})$ by equating the $h^2$ of the two triangles formed when a line is drawn parallel to the bases. Hence, found the necessary variables for $\text{area}(149782.072\mathrm{m})$.
I don't know what to use to determine the dividing line. I do know the area can be proportioned $2:3$, but given a third base(dividing line), and the height of the two resulting trapezoids to be different, I would have to find for the two altitudes first.
How will I be able to do that? Or is there any easier way around?
Best Answer
(1) After constructing the dotted parallel line as shown, we have two //grams with sides of length = 437.
(2) The length of the base of the larger triangle = 138
(3) The length of the base of the smaller triangle = 138* (3/5) = x, say.
(4) The required = x + 437.