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each of equal sides of an isosceles triangle is 4cm greater than its height .If the base of triangle is 24 cm ,calculate the perimeter and the area of the triangle​

 Jun 9, 2022
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Let the height be =  h

 

Each  of the  equal sides  =     sqrt  [ h^2  + (base / 2) ^2 ]  =  sqrt  [ h^2 + 12^2  ]

 

And we know that

 

sqrt  [ h^2  + 12^2  ]  =  h + 4           square both sides

 

h^2 + 144  = h^2 + 8h + 16           rearrange as

 

144 - 16   =  8h

 

128 = 8h

 

128/8 =  h   =   16

 

So....the   sides   = h + 4  =   20

 

The perimeter =  24  + 2(20) =   68  units

 

The area =   (1/2)base * height =   (1/2) (24) (16)  =   192   units^2

 

 

cool cool cool

 Jun 9, 2022

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