the sides of a triangle are 3cm, 4cm, 5cm. find the length of the shortest altitude

Dear Student,

Perimeter of triangle = 3+4+5 = 12 cmSemi-perimeter of triangle = 122 = 6 cmArea of triangle using heron's formula = ss-as-bs-c= 66-36-46-5= 6×3×2×1= 6 cm2Let the length of perpendicular on the side having length 5 cm is x cmThen area of triangle = 12×Base ×Height12×5×x = 6x = 2.4 cmLet the length of perpendicular on the side having length 4 cm is y cmThen area of triangle = 12×Base ×Height12×4×y = 6y = 3 cmLet the length of perpendicular on the side having length 3 cm is z cmThen area of triangle = 12×Base ×Height12×3×z = 6z = 4 cmSo, the length of shortest altitude(or perpendicular) is 2.4 cm

Regards,

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3 cm is the shortest altitude . 
  • -1
Please give the solution also.
 
  • 1
Dear student,
3 cm is the shortest altitude. 
Regards
 
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