Find the missing length.
MG=10cm, NP=4cm, QP= 14cm, MN=____cm
To find the missing length MN, we can use the concept of similar triangles.
First, we need to identify a pair of similar triangles that share two proportional sides. In this case, we can see that triangles MGN and QPN are similar, as they share angle G and have proportional sides MG/NQ and GN/QP.
Now, we can set up a proportion to find the missing length MN. We will use the proportional sides to create the equation.
MG/NQ = GN/QP
Substituting the given values, we have:
10cm/4cm = GN/14cm
To solve for GN, we cross-multiply and then divide:
10cm * 14cm = 4cm * GN
140cm^2 = 4cm * GN
Dividing both sides by 4cm:
GN = 140cm^2 / 4cm
GN = 35cm
Therefore, the missing length MN is 35cm.