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Question
The perimeter of a triangle is 28 cm. One of it’s sides is 8 cm. Write all the sides of the possible isosceles triangles with these measurements.
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Solution
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 – 8 cm = 20 cm
⇒ BC = 10 cm
∴ Sides are 10 cm, 10 cm and 8 cm
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