The sides of triangle are 13cm,14cm, and 15,cm .the length of the shortest altitude is
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Given:

Sides of the triangle are 13cm,14cm, and 15 cm

To find:

Smallest altitude of the triangle

Solution:

Let the sides be

a=13cm,b=14cm,c=15cm

s=a+b+c/2

s=13+14+15/2

s=42/2=21

Area of the triangle

Case (i):

Take, base b = 13cm

But area = 84 cm2

1/2xbxh=84

1/2x13xh=84

h=168/13

h=12.9cm

Case(ii):

Take,base b=14cm

But, area = 84cm2

1/2xbxh=84

1/2x14xh=84

h=168/14

h=12

Case(iii):

Take, base b=16cm

But,area=84cm2

1/2xbxh=84

1/2x15xh=84

h=168/15

h=11.2

Comparing 3 cases,

The smallest altitude of the triangle is 11.2cm

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step-by-step explanation:

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step-by-step explanation: