Printable

2004 AMC 10B Problem 18

Include the solution Back to the problem

2004 AMC 10B Problem 18AMC 10 Step by Step

Name: Date: September 13, 2026

Triangles: Area & Pythagorean · difficulty 3 of 5 · about 5 min · position P16-20

In the right triangle $\triangle ACE$ , we have $AC=12$ , $CE=16$ , and $EA=20$ . Points $B$ , $D$ , and $F$ are located on $AC$ , $CE$ , and $EA$ , respectively, so that $AB=3$ , $CD=4$ , and $EF=5$ . What is the ratio of the area of $\triangle DBF$ to that of $\triangle ACE$ ?

A)
$\frac{1}{4}$
B)
$\frac{9}{25}$
C)
$\frac{3}{8}$
D)
$\frac{11}{25}$
E)
$\frac{7}{16}$

2004 AMC 10B Problem 18

Working