SOLUTION: Find the value of x in each pair of similar figures. 1st picture is a triangle with Q,O,P at each corner. Between Q and O is 5mi, Between Q and P has 6mi. 2nd picture is also a t

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Question 1191368: Find the value of x in each pair of similar figures.
1st picture is a triangle with Q,O,P at each corner. Between Q and O is 5mi, Between Q and P has 6mi.
2nd picture is also a triangle with R,S,T one letter at each corner. Between R and T is xmi, Between T and S has 30mi.
Im trying to help my son with his homework but we dont know how to solve this
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
Find the value of x in each pair of similar figures.
1st picture is a triangle with Q,O,P at each corner.
Between Q and O is 5mi, Between Q and P has 6mi.
2nd picture is also a triangle with R,S,T one letter at each corner.
Between R and T is xmi, Between T and S has 30mi.
Im trying to help my son with his homework but we dont know how to solve this
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Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!
Find the value of x in each pair of similar figures.
1st picture is a triangle with Q,O,P at each corner. Between Q and O is 5mi, Between Q and P has 6mi.
2nd picture is also a triangle with R,S,T one letter at each corner. Between R and T is xmi, Between T and S has 30mi.
Im trying to help my son with his homework but we dont know how to solve this
Are you sure it's not ∆s OPQ and RST? These are usually in alphabetical order.
If so, and you draw the 2 triangles, you'll see that ∆RST is larger, OQ and PQ 
from ∆OPQ correspond to RT and ST of ∆RST, respectively.
Therefore, we get: 
                     ----- Substituting 5, x, 6, and 30 for OQ, RT, PQ and ST, respectively
                    6x = 5(30) ------- Cross-multiplying
                    

OR

You can simply see that ST (30 miles) is 5 times the length of PQ (6 miles).
Therefore, RT (x miles) will also be 5 times OQ (5 miles), or 5(5) = 25 miles
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