Question

The perimeter of an isosceles triangle is 44cm. The ratio of the equal side to it's base is 4:3 . Find the length of the longest altitude
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Answer 1

Given : The perimeter of an isosceles triangle is 44cm. The ratio of the equal side to it's base is 4:3 .

To Find : the length of the longest altitude

Solution:

Let say equal sides are 4x cm

Then base = 3x  cm

Perimeter = 4x + 4x + 3x = 44  

=> 11x = 44

=> x  = 4

Hence equal sides = 4 * 4 = 16 cm

Base = 3 * 4 = 12 cm

As base is shorter than equal sides hence longest altitude will be at base

Altitude at base bisects it

Hence half of base = 12/2 = 6 cm

Length of altitude =  √16² - 6²

= √220

= 2√55 cm

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