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Question

The sides of a triangle are 35 cm, 54 cm, and 61 cm respectively. Find the length of its longest altitude.



Your Answer
A

165cm

Your Answer
B

105cm

Correct Answer
C

245cm

Your Answer
D

28 cm


Solution

The correct option is C

245cm


Thinking Process
(i) First, determine the semi-perimeter, s and then determine the area of the triangle by using Heron’s formula.

(ii) For the longest altitude, take base as the smallest side. Apply the formula,
Area=12×Base×Altitude

(iii) Equate the area obtained using the two formulae and obtain the required height.

Let ABC be a triangle in which sides AB = 35 cm, BC = 54 cm, CA = 61 cm

Now, semi-perimeter of the triangle,
s=a+b+c2=35+54+612=1502=75 cm
[ semiperimeter, s=a+b+c2]
    Area of ΔABC=s(sa)(sb)(sc)
=75(7535)(7554)(7561)
=75×40×21×14
=25×3×4×2×5×7×3×7×2
=5×2×2×3×75=4205 cm2
Also  Area of ΔABC=12×AB×Altitude
      12×35×CD=4205
      CD=420×2535
      CD=245
Hence, the length of altitude is 245 cm

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