Find the two lengths of the triangle by the overall height of the triangle

Question

Can you find the lengths of a / b by the overall height of the triangle?

lulu · Accepted Answer · 2019-06-19T21:26:44.973

1

No. Fix the base segment, that fixes two vertices of the triangle. Imagine a line parallel to the base, at a distance of $800$. Take any point on that line, and make that the third vertex. $a,b$ vary dramatically over that family. Nor is $\frac ab$ constant...there is an isosceles example (for which the ratio is $1$) and a right example (for which it is not).

edited Jun 19 '19 at 21:26

answered Jun 19 '19 at 21:18

lulu

70,402

poetasis · Answer 2 · 2019-07-21T17:05:35.620

0

Given the assumption that the triangle pictured is isosceles:

$a=b=\sqrt{\bigl(\frac{1700}{2}\bigr)^2+800^2}=1167.261753$

edited Jul 21 '19 at 17:05

answered Jul 21 '19 at 16:56

poetasis

6,338

Find the two lengths of the triangle by the overall height of the triangle

2 Answers2