The height and base of a triangle are in ratio 1:3 respectively. If the area of the triangle is 216 cm\(^2\), find the length of the base.

  • A 24cm
  • B 36cm
  • C 72cm
  • D 144cm
waec 1999mathematics

The correct answer is B. 36cm

Area = \(\frac{1}{2} \times base \times height\)

\(height : base = 1 : 3\)

\(\implies base = 3 \times height\)

Let height = h;

Area = \(\frac{1}{2} \times 3h \times h = 216\)

\(3h^2 = 216 \times 2 = 432\)

\(h^2 = \frac{432}{3} = 144\)

\(h = \sqrt{144} = 12.0 cm\)

\(\therefore base = 3 \times 12 = 36 cm\)

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