Question 635832
The sides of similar triangles are proportional. This means that if you make a ratio out of any two corresponding sides, then it works out the same as when you make a ratio out of another pair of corresponding sides.<br>
So to solve your problem we need to figure out which sides correspond to each other. We can do this by trial and error. Let's start by making a ratio out of two sides:
{{{3/5}}}
Now can we form another ratio use a different pair of sides that works out the same? Answer: Yes. We can use
{{{9/15}}} which reduces to {{{3/5}}}<br>
And try as you might, there are no other combinations that result in equal ratios. Since the 3 and 5 inch side correspond and the 9 and 15 inch sides correspond, the 6" side must correspond to the missing side.<br>
We already know what the ratio of that third pair of sides will work out to be, 3/5. We can use this to find the third side:
{{{3/5 = 6/x}}}
Solving this for x we should find that x = 10. So the missing side is 10".