Hello, gunsandroses234!

The diagram attached consists of a rectangle and a triangle ,

so that and are on and respectively, and

a) A particular Sophie diagram has: .

Find the length and width of rectangle

Code:12 X a A o - - - o - - - - - - - o B | *90° * 15 | | * * | b | * 20 * | 16 | * o Y | * * | | * * 25 | 16-b |* * | D o - - - - - - - - - - - o C 12+a

In right triangle

In right triangle

Let: .

In right triangle .[1]

In right triangle

. .

We have: .

Substitute into [1]: .

. . . . . . . . . . . . . .

Therefore: .