An isosceles triangle has base 10 cm, and its area is 60 cm². What are the lengths of the equal sides?

Step-by-step solution

Idea: The area gives the height; the height and half the base are the legs of a right triangle whose hypotenuse is the equal side.

1. 12 × 10 × h = 60 ⇒ 5h = 60 ⇒ h = 12 cm.1 mark
2. The height bisects the base, so half the base = 5 cm.½ mark
3. Equal side = √(5² + 12²) = √169 = 13 cm.1½ marks

Check: Heron with 13, 13, 10: s = 18, √(18 × 5 × 5 × 8) = √3600 = 60 ✓.

Answer to write in the exam

Common mistakes that cost marks

• Using the full base 10 with the height: √(100 + 144) ≈ 15.6 (wrong).
• Forgetting the 12 and getting h = 6.

How this can come in the exam

Try one yourself

An isosceles triangle has base 30 cm and area 300 cm². Find its equal sides.

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