Question

In AABC, D is the midpoint of BC. E is the foot of the perpendicular from A to BC (lie on BC), and F
is the foot of the perpendicular from D to AC. Given that BE = 5, EC =9, and the area of triangle ABC
is 84. Then the value of EF is​

Answer 1

Answer:

LetDEandDFbe the perpendiculars from DonABandACrespectively.

In

△

s

BDE

and

CDF

,

DE=

DF

(Given)

∠BED=

∠CFD=

90

∘

BD=DC (∵

D

is the mid-point of

BC

)

∴

△BDE≅

△CDF

(RHS)

⇒

∠B=

∠C

(cpct)

⇒

AC=

AB

(Sides opp. equal

∠

s are equal)

⇒

△ABC

is isosceles.

Step-by-step explanation:

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