trapezoid question?

In trapezoid ABCD, bases AB = 15 and CD = 30. Points E and F are on AD and BC with EF || AB. If the ratio ofIn trapezoid ABCD, bases AB = 15 and CD = 30. Points E and F are on AD and BC with EF || AB. If the ratio of the area of ABFE to that of EFCD is 13:12, compute EF.

Update:

10 points to the first person who can give me a complete solution.

2 Answers

Relevance
  • 1 decade ago
    Favorite Answer

    Draw a line from point A to line CD.(perpendicular to CD)

    Name the intersection of this line wiyh line EF, G and with line CD, H.

    AG=h1

    GH=h2

    EF=x

    For trapezoid ABFE

    S1=(15+x)*h1/2

    For trapezoid EFCD

    S2=(30+x)*h2/2

    S1/S2=13/12

    ==>

    (15+x)*h1/((30+x)*h2=13/12

    ==>

    h2/h1=12(15+x)/(13(30+x))

    equation #1

    For trapezoid ABCD

    S=S1+S2

    =(15+30)*(h1+h2)/2

    ==>

    (15+x)*h1/2+(30+x)*h2/2=

    45*(h1+h2)/2

    ==>

    (x-15)*h2=(30-x)*h1

    ==>

    h2/h1=(30-x)/(x-15)

    equation #2

    Now consider equations #1 and #2

    ==>

    (30-x)/(x-15)=

    12*(15+x)/((13*(30+x))

    ==>

    13*(900-x^2)=

    12(x^2-225)

    ==>

    x^2=576

    ==>

    x=EF=24

    I believe you owe me 10 pts.

    Sorry for my English. If you correct this solution grammatically and send me my errors I will appreciate that. Thanks.

  • locuaz
    Lv 7
    1 decade ago

    draw a line from point A to line perpendicular to CD

    call the intersection of this line with line EF, G and with line CD, H.

    AG=h1

    GH=h2

    EF=x

    for trapezoid ABFE:

    S1=(15+x)h1/2

    For trapezoid EFCD:

    S2=(30+x)h2/2

    S1/S2=13/12

    (15+x)h1/((30+x)h2=13/12

    h2/h1=12(15+x)/(13(30+x))

    equation 1

    For trapezoid ABCD

    S=S1+S2

    =(15+30)(h1+h2)/2

    (15+x)h1/2+(30+x)*h2/2=

    45(h1+h2)/2

    (x-15)h2=(30-x)h1

    h2/h1=(30-x)/(x-15)

    Source(s): h
Still have questions? Get your answers by asking now.