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Question 4 of 5
Given that rectangle MNOP ~ rectangle STUV, what is the length of Line TU?
Rectangle M N O P is on the left. M P is the bottom segment and is 5 units. Segment O P is the right segment and is 3 units.
Rectangle S T U V is on the right. S V is the bottom segment is x units. Segment U V is the right segment and is 9 units.
A. 18 units
B. 20 units
C. 15 units
D. 11 units
e
I'm sorry, "e" is not a valid answer option for the given question. Can you please provide the question or the options so I can assist you better?
Since the rectangles MNOP and STUV are similar, their corresponding sides are proportional. That is:
MP/UV = NO/ST = OP/SU
We know that MP=5 and OP=3. Also, UV = 9. Substituting these values into the equation, we can solve for ST, which is the length of line TU:
5/9 = NO/ST = 3/SU
Cross-multiplying, we get:
5ST = 9NO and 3ST = 9SU
Dividing the two equations, we get:
5ST/3ST = NO/SU
Simplifying this, we get:
5/3 = NO/SU
Multiplying both sides by SU, we get:
SU x 5/3 = NO
Substituting the values we know, we get:
SU x 5/3 = 5
Solving for SU, we get:
SU = 3
Therefore, TU = SV-SU = 9-3 = 6
So the length of line TU is 6 units.
Therefore, the answer is not given in the options.