SOLUTION: 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
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-> SOLUTION: 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
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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?
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.
The ratio of similarity between the two triangles is 5:7, because DE and DF are corresponding sides of the similar triangles.
So DB and DC are also in the ratio 5:7; and the sum of the two lengths is 48.
I leave it to you to do the arithmetic to find the lengths of BD and CD.
You can put this solution on YOUR website! 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
: =
Cross multiply
5x = 7(48-x)
5x = 336 - 7x
5x + 7x = 336
12x = 336
x = 336/12
x = 28 is length of DC
