The lateral sides of the trapezoid are 7 and 11, and the bases are 5 and 15. A line drawn through the vertex of the smaller base parallel to the larger lateral side cuts off a triangle from the trapezoid. Find the sides of this triangle.

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The specified straight line divides the trapezoid into a triangle and a parallelogram.

## Solution

Let $A D$ and $B C$ be the bases of trapezoid $A B C D$, where

$$
A B=7, B C=5, C D=11, A D=15 \text {. }
$$

Draw a line through vertex $C$ parallel to the side $A B$. Let this line intersect the base $A D$ at point $K$. Then $A B C K$ is a parallelogram. Therefore,

$$
C K=A B=7, D K=A D-A K=A D-B C=15-5=10 .
$$

## Answer

$7,10,11$.