Question

In∆ABC,angle C=90 and de perpendicular to the ab. If BC=12cm,ad=10cm and DC=6cm,find the length of AE

Answer 1

Step-by-step explanation:

To Prove : △ADE∼△ACB

Proof :

(i) In △ADE and △ACB

    (1) ∠A=∠A                [common]

    (2) ∠AED=∠ABC=90o  (given)

    ∴    △ADE∼△ACB  [AA axiom]

(ii) (AC)2=(AB)2+(BC)2

     169=(AB)2+25

     AB=12cm

∵   △ADE∼△ACB

∴   BCDE=ACAD=ABAE

∴     BCDE=ABAE

              5DE=124

              DE=1220=35=132cm

Now, ACAD=