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The ratio of bar(DB) to bar(EF) is 4 to...

The ratio of `bar(DB)` to `bar(EF)` is 4 to 9. If `bar(DF)=2`, what is the distance from D to the midpont of `bar(EF)` ?

A

`(9)/(13)`

B

`(12)/(13)`

C

`(14)/(13)`

D

`(17)/(13)`

Text Solution

Verified by Experts

The correct Answer is:
D
Mark up the figure :

The brackets around the 4 and the 9 are meant to show that they're proportions, not actual lengths. Since the ratio of `bar(DE)` to `bar(EF)` is 4 9, you can say that 4 parts out of 13 are in `bar(DE)` and 9 parts out of 13 are in `bar(EF)`.
Because the whole length `bar(DF)=2, bar(DE)=(4)/(13)xx2=(8)/(13)`
and `bar(EF)=(9)/(13)xx2=(18)/(13)`. The midpoint of `bar(EF)` divides it in half, so each half length is half of `(18)/(13)`, which is `(9)/(13)`. The length you're looking for is `(8)/(13)+(9)/(13)=(17)/(13)`.
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Knowledge Check

  • What is the length of bar(QR) ?

    A
    `5`
    B
    `(5sqrt2)/2`
    C
    `10sqrt2`
    D
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  • In the circle above with diameter d, chords bar(PQ) and bar(TU) are parallel to diameter bar(RS) . If bar(PQ) and bar(TU) are each (3)/(4) of the length of bar(RS) , what is the distance between chords bar(PQ) and bar(TU) in terms of d?

    A
    `(dsqrt7)/(8)`
    B
    `(dsqrt7)/(4)`
    C
    `(pid)/(4)`
    D
    `(3pid)/(4)`

  • In the figure below, ABCD is a rectangle, EFGH is a square, and bar(CD) is a diameter of a semicircle. Point K is the midpoint of bar(CD) . Point J is the midpoint of both bar(AB) and bar(EF) . Points E and F lie on bar(AB) . The 3 given lengths are in meters. The length of bar(EH) is what precent of the length of bar(AD) ?

    A
    0.156
    B
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    C
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    D
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