ABC is an isosceles triangle with height AD = 4 cm and base BC = 6 cm. Find the perimeter of the triangle.

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Solution

If ABC is an isosceles triangle and AD is the height of the triangle then AD is also the median of the triangle, So D is the midpoint of BC

DC $= \frac{B C}{2} = \frac{6}{2} = 3 c m$

Triangle ADC is a right angled triangle

Applying pythagoras theorem in triangle ADC

$A D^{2} + D C^{2} = A C^{2}$
$4^{2} + 3^{2} = A C^{2}$
$16 + 9 = A C^{2}$
$25 = A C^{2}$
$A C = 5 c m$

Similarly $A B = 5 c m$

Perimeter of the triangle = AB + BC + CA = 5 + 6 + 5 = 16 cm

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