Question

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

Answer 1

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$=\frac{BC}{2}=\frac{6}{2}=3cm$

Triangle ADC is a right angled triangle

Applying pythagoras theorem in triangle ADC

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

Similarly $AB=5cm$

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