Question

The sides of a triangle are 35 cm, 54 cm and 61 cm respectively. Find the

length of its longest altitude.​

Answer 1

Step-by-step explanation:

s=

2

a+b+c

=

2

35+54+61

=75

Area, A=

s(s−a)(s−b)(s−c)

=

75(75−35)(75−54)(75−61)

=420

5

cm

2

Now, Area of the triangle is also given as A=

2

1

×a×h

Where, h is the longest altitude.

Therefore,

2

1

×a×h=420

5

Hence, h=24

5

cm

Answer 2

Answer:

s=2a+b+c=235+54+61=75

Area, A=s(s−a)(s−b)(s−c)=75(75−35)(75−54)(75−61)=4205cm2  

Now, Area of the triangle is also given as A=21×a×h

Where, h is the longest altitude.

Therefore, 21×a×h=4205

hence H=245cm

hope it help you