Answer: X = 28
Step-by-step explanation: The diagram shows a triangle which is actually in fact, two triangles placed into each other. The first one is triangle APR (the larger one) while the second one is triangle CDR (the smaller one).
Also the diagram shows line AP as being parallel to line CD. That makes triangle APR similar to triangle CDR.
We can now determine the ratios of the similar sides
If triangle APR = triangle CDR, then
Line PD/DR = AC/CR or
PD/PR = AC/AR or
CD/RD = AP/RP
Therefore to calculate X, we use the ratio,
PD/DR = AC/CR
15/42 = 10/x
{we reduce the left hand side to it's simplest form}
5/14 = 10/x
When we cross multiply we now have
5x = 14 × 10
5x = 140
Divide both sides of the equation by 5
x = 28
