Question

What is the length of DE

Answer 1

Answer:

DE = 20units

Step-by-step 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,

$\frac{cd}{cb} = \frac{ce}{ca} = \frac{de}{ab} \\ therefore \: \frac{8}{4} = \frac{8}{4} = \frac{de}{10 } \\ therefore \\ \frac{2}{1 } = \frac{de}{10 } \\ de \: = 2 \times 10 = 20units$