The perimeter of an isosceles triangle is 42 cm and its base is

1
1
2

times, each of the equal sides. The area of the triangle is ____

c
m
2

.

Question

The perimeter of an isosceles triangle is 42 cm and its base is

1
    1
    2

times, each of the equal sides. The area of the triangle is ____

c
    m
    2

.

Accepted Answer

The perimeter of an isosceles triangle is 42 cm and its base is

1
    1
    2

times, each of the equal sides. The area of the triangle is 71.43

c
    m
    2

.Given the perimeter of an isosceles triangle is 42 cm and its base is

1
    1
    2

times, each of the equal sides.Let the length of 2 equal sides = x.Therefore, the length of base is,

b=1
    1
    2
   
   x

⇒b=
      3
      2
     
     x

⇒b=1.5xcm

Consider an isosceles triangle ABC with median AD,Now the perimeter of triangle is,

perimeter=AB+BC+CA

⇒42=x+1.5x+x

⇒42=3.5x

⇒x=12cm

The length of equal sides = 12 cm,The length of base = 18 cm,As the median divides the side into two equal parts, so length of BD=9cmCalculating the height of median AD, using Pythagoras theorem,

hypotenuse
     
    2
   
   =

base
     
    2
   
   +

perpendicular
     
    2

A
      B
      2
     
     =A
      D
      2
     
     +B
      D
      2

⇒
      12
      2
     
     =A
      D
      2
     
     +
      9
      2

⇒A
      D
      2
     
     =144−81

⇒A
      D
      2
     
     =63

⇒AD=3
      7

Now the area of triangle is,

A=
      1
      2
     
     ×Base×Height

⇒A=
      1
      2
     
     ×18×3
      7

⇒A=9×3
      7

⇒A=27
      7

A = 71.43

c
    m
    2

The area of the triangle is 71.43

c
    m
    2

.

The perimeter of an isosceles triangle is 42 cm and its base is $112$ times, each of the equal sides. The area of the triangle is ____ $c m 2$ .

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The perimeter of an isosceles triangle is 42 cm and its base is 1 1 2 times, each of the equal sides. The area of the triangle is ____ c m 2 .

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The perimeter of an isosceles triangle is 42 cm and its base is $112$ times, each of the equal sides. The area of the triangle is ____ $c m 2$ .