Geometry Problem from Singapore ( 1 )

Let the diameter of the semi-circle be $x$ .

Now, looking at the top half of the figure, the length of the line in the middle can be represented as $3x + 24$ .

Looking at the bottom half of the figure, the length of the middle line can be expressed as $2x + 60$ .

Equating the two, we get that $x = \boxed{36}$ .

Let, $\text{d}$ be the diameter of the semi-circle. Then,

$\text{d+12+d+12+d=22+d+16+d+22}$

$\text{3d+24=2d+60}$

$\boxed{\text{d=36}}$

Online Solution