Abc similar to def the area of abc is 45cm and the area of triangle def is 20cm one side of triangle abc is 3.6cm the the length of correspo

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Abc similar to def the area of abc is 45cm and the area of triangle def is 20cm one side of triangle abc is 3.6cm the the length of corresponding side of triangle def is

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Thanh Hà 5 years 2021-07-30T03:52:32+00:00 1 Answers 36 views 0

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  1. Nem
    0
    2021-07-30T03:54:12+00:00
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    Answer:

    2.4cm

    Step-by-step explanation:

    the area of a triangle is

    baseline × height / 2

    that means two lengths of the triangle have to be multiplied.

    and to have 2 similar triangles means that all lengths inside one triangle are the corresponding lengths inside the other triangle multiplied by the scaling factor f.

    multiplying 2 if these lengths with each other means also including the square of the scaling factor (multiplying with the scaling factor twice).

    so, if the area of triangle 1 is

    “baseline 1” × “height 1” / 2 = 45 cm²

    then the area of triangle 2 is

    “baseline 2” × “height 2” / 2 =

    = “baseline 1″×f × “height 1″×f /2 =

    = “baseline 1” × “height 1” × f² / 2 =

    = (“baseline 1” × “height 1” / 2) × f² =

    = 45 × f² = 20 cm²

    f² = 20/45 = 4/9

    f = 2/3

    so, for a side of ABC being 3.6cm long, that means the corresponding side in DEF is

    3.6 × f = 3.6 × 2/3 = 7.2/3 = 2.4cm

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