Question

What is the length of DE

Answer 1

DE = 20units

Explanation:

In Δ ABC,

angle A is congruent to angle B.... (given)

therefore, ΔABC is an isoceles triangle.

therefore, CA = CB..... (side opposite to congruent angles are congruent in an isoceles triangle)

therefore, CB = 4 units

In ΔCDE,

angle D is congruent to angle E.... (given)

therefore, ΔCDE is an isoceles triangle.

therefore, CD = CE

therefore, CD = 8 units

ΔCDE ~ ΔCBA

therefore,

`(cd)/(cb) = (ce)/(ca) = (de)/(ab) \\ therefore \: (8)/(4) = (8)/(4) = (de)/(10 ) \\ therefore \\ (2)/(1 ) = (de)/(10 ) \\ de \: = 2 * 10 = 20units`