Printable

2005 AMC 10A Problem 25

Include the solution Back to the problem

2005 AMC 10A Problem 25AMC 10 Step by Step

Name: Date: September 13, 2026

Triangles: Area & Pythagorean · difficulty 4 of 5 · about 4 min · position P21-25

In $\triangle ABC$ we have $AB = 25$ , $BC = 39$ , and $AC = 42$ . Points $D$ and $E$ are on $\overline{AB}$ and $\overline{AC}$ respectively, with $AD = 19$ and $AE = 14$ . What is the ratio of the area of triangle $ADE$ to the area of the quadrilateral $BCED$ ?

A)
$\frac{266}{1521}$
B)
$\frac{19}{75}$
C)
$\frac{1}{3}$
D)
$\frac{19}{56}$
E)
$1$

2005 AMC 10A Problem 25

Working