Question

The perimeter of a triangle is 28 cm. One of its sides is 8 cm. Write all the sides of the possible isosceles triangles with these measurements.

Answer 1

Let ∆ABC be an isosceles triangle, where AB = 8 cm

Case I:

If AB = BC

AB = BC = 8 cm

Perimeter of the triangle ABC = 28 cm

⇒ AB + BC + CA = 28 cm

⇒ 8 cm + 8 cm + CA = 28 cm

⇒ 16 cm + CA = 28 cm

⇒ CA = 28 cm – 16 cm = 12 cm

∴ Sides are 8 cm, 8 cm and 12 cm

Case II:

If BC = CA

Perimeter of the triangle ABC = 28 cm

⇒ AB + BC + CA = 28 cm

8 cm + 2BC = 28 cm

⇒ 2BC = 28 cm – 8cm = 20 cm

⇒ BC = 10 cm

∴ Sides are 10 cm, 10 cm and 8 cm