Question

In right triangle ABC shown to the right, the lengths of AB, BC, and BE are 20, 15, and 6, respectively. What is the length of DE?

Answer 1

`DE=12`

Explanation:

From the question we are told that:

`AB=20\\\\BC=15\\\\BE =6`

Generally the equation for the similar triangles is mathematically given by

`(AB)/(BC) =(DE)/(EC)`

Where

`EC = BC - BE \\\\EC= 15-6 \\\\EC= 9`

Therefore

`(20)/(15) =(DE)/(9)`

`(20*9)/(15) =DE`

`DE=12`

Answer 2

12

Explanation:

Assuming the diagram is thesame as the one attached,

From the diagram,

Triangle ABC is similar to Triangle DEC

ΔABC is similar to ΔDEC

Note: In similar triangle, ratio of corresponding sides are equal

Therefore,

line(AB) /line(DE) = line(BC)/line(EC).................... Equation 1

Given: AB = 20, BC = 15, EC = BC-BE = (15-6) = 9

Substitute these values into equation 1 and solve for Line DE

20/DE = 15/9

DE = (20×9)/15

DE = 12.

Hence line DE = 12.