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Question

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=BC2=62=3 cm

Triangle ADC is a right angled triangle

Applying pythagoras theorem in triangle ADC

AD2+DC2=AC2
42+32=AC2
16+9=AC2
25=AC2
AC=5 cm

Similarly AB=5 cm

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

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