Question

In the given figure, angle CAB = angle CED, CD = 8 cm, CE = 10 cm, BE = 2 cm, AB = 9 cm, AD = b and DE = a, the value of a + b is

Answer 1

Answer:

the value of a+b = 13 cm

Step-by-step explanation:

in ΔDCE & ΔABC

∠C = ∠C      - common Angle

∠CED = ∠CAB   ( given)

=> ∠CDE = ∠CBA  ( if two nagles are equal then third angle will also be equal)

ΔDCE ≅ ΔABC

CE / AC  = DC/BC  =  DE/AB

=> CE/(CD + AD) =  DC/(BE + EC)  = DE/AB

=> 10/(8 + b) = 8/(2 + 10)  = a/9

Using first two

10/(8 + b) = 8/12

=> 120 = 64 + 8b

=> 8b = 56

=> b = 7

Using last two

8/(2 + 10)  = a/9

=> 8/12 = a/9

=> 72 = 12a

=> a = 6

a + b = 7 + 6 = 13 cm

the value of a+b = 13 cm.

hope you understand