Question

Find the length of RA. A. 42 B. 84 C. 14 D. 7

Answer 1

Answer:

B) 84

Step-by-step explanation:

ΔLRU ≅ ΔLAU   {SAS congruent}

Therefore, UA = UR    {CPCT}

 6m = 3m +21

Subtract 3m from both sides

6m - 3m = 3m + 21 -3m

        3m = 21

Divide both sides by 3

    3m/3 = 21/3

m = 7

RA = RU + UA

    = 3m + 21 + 6m {add like terms}

    = 9m + 21   {Plug in m =7}

    = 9*7 + 21

    = 63 + 21

RA = 84 units

Answer 2

Answer:

$\large \boxed{\mathrm{B. \ 84}}$

Step-by-step explanation:

$LU$ bisects $RU$ and $UA$.

$RU=UA$

$3m+21=6m$

Solve for m.

Subtract 3m from both sides.

$21=3m$

Divide both sides by 3.

$7=m$

Calculate $RA$.

$RA=3m+21+6m$

$RA=9m+21$

Put m = 7.

$RA=9(7)+21$

$RA=63+21$

$RA=84$