The length of the base and the area of an isosceles triangle are respectively 8 cm and 12 cm². The length of each equal side is :

1. 15 cm

2. 10 cm

3. 6 cm

4. 5 cm

ABC is an isosceles triangle with AB = AC and base (BC) = 8 cm.

Area of a triangle = $\dfrac{1}{2}$ × base × height

Area of triangle ABC = $\dfrac{1}{2}$ × BC × AD

⇒ 12 = $\dfrac{1}{2}$ × 8 × AD

⇒ AD = $\dfrac{24}{8}$ = 3 cm.

In an isosceles triangle, the perpendicular from the common vertex to the base, bisects the base.

∴ BD = DC = $\dfrac{BC}{2} = \dfrac{8}{2}$ = 4 cm.

In triangle ABD,

⇒ Hypotenuse² = Base² + Height²

⇒ AB² = BD² + AD²

⇒ AB² = 4² + 3²

⇒ AB² = 16 + 9

⇒ AB² = 25

⇒ AB = $\sqrt{25}$

⇒ AB = 5 cm.

∴ AB = AC = 5 cm.

Hence, option 4 is the correct option.