Question

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​

Answer 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:

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