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19 July, 06:33

The triangles ABC and DFG are similar and the ratio of their corresponding sides is 6:5. The area of the triangle ABC is greater than the area of the triangle DFG by 77 cm2. Find the areas of these triangles.

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  1. 19 July, 06:53
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    Area of triangle DFG = 175

    Area of triangle ABC = 252

    Step-by-step explanation:

    It is given that,

    The triangles ABC and DFG are similar and the ratio of their corresponding sides is 6:5. The area of the triangle ABC is greater than the area of the triangle DFG by 77 cm2.

    Let area of triangle DFG = x then area of triangle ABC = x + 77

    To find the area of 2 triangles

    ar (DFG) / ar (ABC = (5/6) ²

    x / (x + 77) = 25/36

    36x = 25x + (25 * 77)

    36x - 25x = 25 * 77

    11x = 25 * 77

    x = 175

    Therefore area of triangle DFG = 175

    Area of triangle ABC = 175 + 77 = 252
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