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
<pre>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: {{{matrix(1,3, OQ/RT, "=", PQ/ST)}}}
                    {{{matrix(1,3, 5/x, "=", 6/30)}}} ----- Substituting 5, x, 6, and 30 for OQ, RT, PQ and ST, respectively
                    6x = 5(30) ------- Cross-multiplying
                    {{{highlight_green(matrix(1,6, x, "=", 5(30)/6, "=", 25, miles))}}}

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</pre>