Question

in the fig. angle ACB = angle AED =90°. The sum of length of AE & DE is ​

Answer 1

Answer:

OPTION (C)

Step-by-step explanation:

Given : ΔACB is right angled triangle at C = 90°.

From the figure : BC = 12 cm , AD=3 cm, DC = 2 cm.

AC = AD + DC = 3 +2= 5 cm

In ∆ACB,

AB² = AC² + BC² (by pythagoras theorem)

AB² = 5² + 12²

AB² = 25 + 144 = 169

AB= √169 = 13  

AB = 13 cm

In  ΔABC & ΔADE

∠BAC = ∠DAE  (common)

∠ACB = ∠AED   (each 90°)

ΔABC∼ΔADE (by A-A similarity criterion),

AB/AD = BC/DE = AC/AE

[Since corresponding sides of two similar triangles are proportional]

13/3 = 12/ DE = 5/AE

13/3 = 12/DE

13 DE = 12×3  

DE = 36/13

13/3 = 5/AE

13 AE = 5×3

AE = 15/13

Hence, the length of DE= 36/13 & AE = 15/13

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Answer:

A) 5.6cm

Step-by-step explanation:

AC =4+2=6

AB=√BC^2 + AC^2 = √8^2+6^2 =√100=10cm

∆AED ~ ∆ABC

so, DE/AC = AD/AB

DE/6=4/10

DE=2.4cm

AE=√AD^2 - DE^2

AE =√4^2 - 2.4^2

AE=3.2 CM

•°• AE+DE =3.2+2.4 = 5.6cm

..(A) is correct answer