If I know that one of the heights of a rhombus splits its longer diagonal in 2 segments equal to 7 and 11, how can I find the length of the base of the rhombus?
2026-04-13 09:45:24.1776073524
Problem involving rhombus and its diagonals and height
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Let half of the shorter diagonal be x, the length of a side of the rhombus b, the said height be h, a known quantity according to the question.
We can setup 2 equations:-
(1) area of the rhombus by (4 times the green triangle with the unknown x) = area of the rhombus by (b * h with the unknown b)
(2) Use Pythagoras to relate 9, x and b
Eliminating x from (1) and (2), we will obtain a quadratic equation in b.
Solving it, we get the required.