Question

18. In AABC, D and E are points on the sides AB and AC respectively such
that DE I BC. IT AD/DB = 3/4 and AC = 15 cm find AE.
a. 6.43 cm
b. 6.41 cm
C. 6.20 cm
d. 6.50 cm


pasagoot naman pooo TT ,,need po ng solution ༎ຶ‿༎ຶ​

Answer 1

Answer:

★ Question :-

In AABC, D and E are points on the sides AB and AC respectively such

that DE I BC. IT AD/DB = 3/4 and AC = 15 cm find AE.

★ Answer :-

we have

$\frac{ad}{db} = \frac{3}{4} and \: de || bc$

Therefore by basics proportionality theorem we have

$\frac{ad}{db} = \frac{ae}{ec}$

Adding 1 on both side we get

$\frac{ad}{db} + 1 = \frac{ae}{ec} + 1$

$\frac{3}{4} + 1 = \frac{ae + ec}{ec}$

$\frac{3 + 4}{4} = \frac{ac}{ec}$

$= \frac{7}{4} = \frac{15}{ec}$

$ec = \frac{15 \times 4}{7}$

$ec = \frac{60}{7}$

Now AE + EC = AC

$ae + \frac{60}{7} = 15$

$ae \: = \: 15 - \frac{60}{7}$

$\frac{105 - 60}{7}$

$= \frac{45}{7}$

$= answer \: 6.43cm$

hope it was helpful to you.....★