in the adjacent figure triangle ABC is right angled at C and D E prove that triangle ABC~triangle ADE and hence find the lengths of AEand DE
Answers
Answered by
1
SOLUTION
In ΔACB, by Pythagoras theorem
AB2 = AC2 + BC2
⇒ AB2 = (5)2 + (12)2
⇒ AB2 = 25 + 144 = 169
⇒ AB = 169 = 13 cm
In ΔAED and ΔACB
∠A = ∠A [Common]
∠AED = ∠ACB [Each 90°]
Then, ΔAED ~ ΔACB [By AA similarity]
∴AEAC=DECB=ADAB [Corresponding parts of similar Δ are proportional]
⇒AE5=DE12=313
⇒AE5=313 and
DE12=313
AE=1513 cm and
DE=3613 cm
Step-by-step explanation:
hope it works..
Similar questions