Question

The length of the sides of a triangle are 15 cm, 12 cm and 9 cm.

Find the length of the perpendicular from the opposite vertex to

the longest side​

Answer 1

Answer:

Explanation:

It is clear that the triangle is a right angled triangle.

Let AB=12 cm BC=5 cm and AC=13 cm

Now a perpendicular is drawn from A to AC.

a

r

(

A

B

C

)

=

½

A

B

⋅

B

C

=

½

C

A

⋅

B

D

.

B

D

=

A

B

⋅

B

C

C

A

Putting the respective values of the sides we get,

B

D

=

60

13

cm

Answer 2

Answer:

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Step-by-step explanation:

a=15,b=12,c=9

s=1/2(a+b+c) =15

Area of the triangle,A =√s(s-a)(s-b)(s-c)

A= √15(15-15)(15-12)(15-9)

A=√15×0×3×6

A=270cm2

Let, P be the length of the perpendicular from vertex D on the side BC then,

A=1/2×13×p

2A = 13p

2×270 = 13p:- P=180/13 cm

Hence,length of perpendicular from the opposite vertex to the side whose length is 13 cm is (180/13) cm.