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The height and base of a triangle are in ratio 1:3 respectively. If the area…

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
Correct Answer: Option B
Explanation

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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