Mathematics
Grade9
Easy

Question

The areas of two similar triangles are 45 square cm and 80 square cm. The sum of their perimeters is 35 cm. Find the perimeter of each triangle.

  1. 10 cm and 25 cm
  2. 15 cm and 20 cm
  3. 14 cm and 21 cm
  4. 16 cm and 19 cm

hintHint:

Find the corresponding side length and then find the perimeter

The correct answer is: 15 cm and 20 cm


    Let the two triangles, triangle subscript 1 and triangle subscript 2 and let the scale factor of the two similar triangles
    Then, fraction numerator area space triangle subscript 1 over denominator area space triangle subscript 2 end fraction equals open parentheses a over b close parentheses squared
45 over 80 equals open parentheses a over b close parentheses squared
    a : b  is the reduced for of the scale factor, 3:4 is then the reduced form of the comparison of the perimeters.
    9 over 16 equals open parentheses straight a over straight b close parentheses squared
    Reduce the fraction
    3 over 4 equals straight a over straight b
    Take square roots of both sides.
    Let 3x  = perimeter of triangle subscript 1
    and 4x = perimeter of triangle subscript 2
    Then 3x + 4x = 35 (The sum of the perimeters in 35 cm)
    7x = 35
    x = 5
    So,
    Perimeter triangle subscript 1 = 3(5) = 15 cm
    Perimeter triangle subscript 2 = 4(5) = 20 cm

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