Take the 2-minute tour ×  I have two right triangles One is a
6-8-10 and inside is a 3-4-5 and the space between the two
triangles is a uniform amount.  I made a really awkward and
weird pic of the diagram and I need to solve for X enter image
description here  How would I go about solving this? I couldn't
figure out any good approaches.  share|improve this question
Hint: draw in some lines and look for similar triangles inside
the bigger triangle. –  Vitaly Lorman Mar 10 '11 at 1:07
@VitalyLorman , I'm not sure I follow –  qwertymk Mar 10 '11 at
1:15  4 Answers 4  up vote 14 down vote accepted  Draw lines
connecting the "respective vertices". Add up the areas to solve
for $x$.  enter image description here  Area of a right triangle
with the non-hypotenuse sides being $a$ and $b$ is
$\frac{1}{2}(a \times b)$ while the area of a trapezium with
parallel sides being $a$ and $b$ and the height being $h$ is
$\frac{1}{2}h(a+b)$  $$\frac{1}{2}x(5+10) + \frac{1}{2}x(3+6) +
\frac{1}{2}x(4+8) + \frac{1}{2}(3 \times 4)