Triangles · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
3. In an isosceles triangle, the perimeter is 40 cm and the base is 16 cm. Find the length (in cm) of each equal side.
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Answer: B) 12
Two equal sides + base = perimeter. 2x + 16 = 40 → 2x = 24 → x = 12 cm.
4. In triangle ABC, D is a point on side BC. Given angle B = 50° and angle BAD = 30°, find angle ADC in degrees.
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Answer: C) 80
Angle ADC is an exterior angle of triangle ABD at D, so it equals the sum of the two opposite interior angles of that triangle: angle B + angle BAD = 50 + 30 = 80°. Check the long way: angle ADB = 180 − 50 − 30 = 100°, and angle ADC = 180 − 100 = 80°. Trap: answering 100°, which is the adjacent angle ADB, not the one asked for.
5. Two sides of a triangle measure 7 cm and 11 cm. Between which two values must its perimeter lie?
- ABetween 18 cm and 36 cm
- BBetween 22 cm and 36 cm
- CBetween 4 cm and 18 cm
- DBetween 22 cm and 40 cm
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Answer: B) Between 22 cm and 36 cm
The third side must satisfy 11 − 7 < x < 11 + 7, that is 4 < x < 18. The perimeter is 7 + 11 + x = 18 + x, so it lies between 18 + 4 = 22 cm and 18 + 18 = 36 cm. Trap: quoting 4 cm to 18 cm, which is the range of the THIRD SIDE and not of the perimeter — the two known sides still have to be added back on.