MathDB

In this figure

\angle RFS = \angle FDR

FD = 4

inches,

DR = 6

inches,

FR = 5

inches,

FS = 7\dfrac{1}{2}

inches. The length of

RS

, in inches, is:
[asy] import olympiad; pair F,R,S,D; F=origin; R=5*dir(aCos(9/16)); S=(7.5,0); D=4*dir(aCos(9/16)+aCos(1/8)); label("

F

",F,SW);label("

R

",R,N); label("

S

",S,SE); label("

D

",D,W); label("

7\frac{1}{2}

",(F+S)/2.5,SE); label("

4

",midpoint(F--D),SW); label("

5

",midpoint(F--R),W); label("

6

",midpoint(D--R),N); draw(F--D--R--F--S--R); markscalefactor=0.1; draw(anglemark(S,F,R)); draw(anglemark(F,D,R)); //Credit to throwaway1489 for the diagram[/asy]

<span class='latex-bold'>(A)</span>\ \text{undetermined} \qquad <span class='latex-bold'>(B)</span>\ 4\qquad <span class='latex-bold'>(C)</span>\ 5\dfrac{1}{2} \qquad <span class='latex-bold'>(D)</span>\ 6 \qquad <span class='latex-bold'>(E)</span>\ 6\dfrac{1}{4}

Problem Statement