Question

V is the midpoint of RU and T is the midpoint of SU If RS=w and TV=w–23, what is the value of w?

Answer 1

ST+TU=SU

ST=TU

SU/2=ST=TU

5x-2=3x-4

2x=-2

x=-1

ST=5x-2=5(-1)-2=-5-2=-7 --->|ST|=7

TU=3x-4=3(-1)-4=-3-4=-7 --->|TU|=7

ST+TU=SU ---> 7+7=14

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Answer 2

• w = 46

Explanation:

• V is the midpoint of RU, so VU = 1/2 RU
• T is the midpoint of SU, so UT = 1/2 SU

And we have:

• RS = w, or
• RU + SU = w

Also we have:

• TV = w - 23,

or substitute as above given:

• VU + UT = w - 23
• 1/2 RU + 1/2 SU = w - 23
• 1/2 (RU + SU) = w - 23
• 1/2 w = w - 23
• w - 1/2 w = 23
• 1/2 w = 23
• w = 23*2
• w = 46