Question

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

Answer 1

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

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`

Answer 2

B) 84

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