Question 1120260
<br>
Triangles BED and CFD are similar: the angles at C and F are right angles; and the angles at B and C are the congruent base angles of the isosceles triangle.<br>
The ratio of similarity between the two triangles is 5:7, because DE and DF are corresponding sides of the similar triangles.<br>
So DB and DC are also in the ratio 5:7; and the sum of the two lengths is 48.<br>
I leave it to you to do the arithmetic to find the lengths of BD and CD.