# A triangle has 3 sides 35cm.,54cm,and 61cm. long .Find it's area. Also, find he smallest of it's altitude.

• 4

a = 35cm

b = 54cm

c = 61cm

s = a+b+c / 2

= 35+54+61 / 2

= 150 / 2

= 75

area = whole root 75(75-35)(75-54)(75-61)

= whole root75*40*21*14

= whole root25*3*2*5*4*7*3*7*2

= 5*3*2*2*7root5

= 420root5

now,

area = 1/2bh

= 1/2*35*h = 420root5

= h = 420*2*root5 / 35

= h = 24root5

• 11

a = 35cm

b = 54cm

c = 61cm

s = a+b+c / 2

= 35+54+61 / 2

= 150 / 2

= 75

area = whole root 75(75-35)(75-54)(75-61)

= whole root75*40*21*14

= whole root25*3*2*5*4*7*3*7*2

= 5*3*2*2*7root5

= 420root5

now,

area = 1/2bh

= 1/2*35*h = 420root5

= h = 420*2*root5 / 35

= h = 24root5

• 3

a = 35cm

b = 54cm

c = 61cm

s = a+b+c / 2

= 35+54+61 / 2

= 150 / 2

= 75

area = whole root 75(75-35)(75-54)(75-61)

= whole root75*40*21*14

= whole root25*3*2*5*4*7*3*7*2

= 5*3*2*2*7root5

= 420root5

now,

area = 1/2bh

= 1/2*35*h = 420root5

= h = 420*2*root5 / 35

= h = 24root5

• 3

a = 35cm

b = 54cm

c = 61cm

s = a+b+c / 2

= 35+54+61 / 2

= 150 / 2

= 75

area = whole root 75(75-35)(75-54)(75-61)

= whole root75*40*21*14

= whole root25*3*2*5*4*7*3*7*2

= 5*3*2*2*7root5

= 420root5

now,

area = 1/2bh

= 1/2*35*h = 420root5

= h = 420*2*root5 / 35

= h = 24root5

• 3

a = 35cm

b = 54cm

c = 61cm

s = a+b+c / 2

= 35+54+61 / 2

= 150 / 2

= 75

area = whole root 75(75-35)(75-54)(75-61)

= whole root75*40*21*14

= whole root25*3*2*5*4*7*3*7*2

= 5*3*2*2*7root5

= 420root5

now,

area = 1/2bh

= 1/2*35*h = 420root5

= h = 420*2*root5 / 35

= h = 24root5

• -2

a = 35cm

b = 54cm

c = 61cm

s = a+b+c / 2

= 35+54+61 / 2

= 150 / 2

= 75

area = whole root 75(75-35)(75-54)(75-61)

= whole root75*40*21*14

= whole root25*3*2*5*4*7*3*7*2

= 5*3*2*2*7root5

= 420root5

now,

area = 1/2bh

= 1/2*35*h = 420root5

= h = 420*2*root5 / 35

= h = 24root5

• 10
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