geometry

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In similar triangles ABC and DEF, corresponding sides AB and DE equal 15 and 12, respectively. If the perimeter of triangle ABC=40, what is the perimeter of triangle DEF

  • geometry -

    because of similar triangles, each side of triangle DEF is 12/15 or 4/5 as long as the corresponding sides of ABC
    in first
    a+b+15 = 40
    a+b = 25

    in DEF
    perimeter = e+d + 12
    = (4/5)b + (4/5)a + 12
    = (4/5)(b+a) + 12
    = (4/5)(25) + 12
    = 32

    Or
    by just "common sense" if each side is 4/5 of the old triangle then the new perimeter is (4/5) of 40 or 32

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