Question 1120260
Given: Isosceles triangle ABC with AB = AC
Point E is between AB, Point F is between AC and Point D between BC
Angles BED and DFC are both right angles
The ratio of DE to DF is 5 : 7
The length of BC is 48 
Question: What is the length of DC?
:
the 3 angles of right triangles BDE and CDF are equal, they are similar triangles
therefore the sides are in the ratio of 5:7
let x = the length of DC, 
then
(48-x) = the length of BD
:
{{{x/(48-x)}}} = {{{7/5}}}
Cross multiply
5x = 7(48-x)
5x = 336 - 7x
5x + 7x = 336
12x = 336
x = 336/12
x = 28 is length of DC