Angle and perimeter ratios in similar triangles

Angle and perimeter ratios in similar triangles

Secondary 2
8 marks
TGM Original Questions

Triangle \(ABC\) has angles \(\angle A=6x^\circ\), \(\angle B=5x^\circ\), and \(\angle C=4x^\circ\). Its longest side is \(BC=10\) cm.

  1. Find \(x\).[2]
  2. Find the largest angle.[2]
  3. A triangle \(PQR\) is similar to \(ABC\).
    1. State its smallest angle.[2]
    2. If its longest side is \(4\) cm, find perimeter \(ABC\) : perimeter \(PQR\).[2]

Solution:

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Answer:(a) \(12\) (b) \(72^\circ\) (c)(i) \(48^\circ\) (ii) \(5:2\).

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