Question

In the diagram below, OP is parallel to LM. If LM is twice the length of ON, LN = 7, and OP = 4, find the length of ON. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.

Answer 1

To find the length of ON in a parallelogram where OP is parallel to LM, use the fact that LM is twice the length of ON. Set up a proportion between ON and MN to find ON's length.

Step-by-step explanation:

To find the length of ON, we can use the fact that OP is parallel to LM. Since LM is twice the length of ON, we can set up the following equation: LM = 2 * ON. Given that LN is 7 and OP is 4, we can use these values to solve for ON.

We know that LN = LM + MN. Since LN is 7 and LM is 2 * ON, we can substitute these values into the equation and solve for MN: 7 = 2 * ON + MN.

Now we can use the fact that OP is parallel to LM to set up a proportion between ON and OP: ON/4 = MN/2. Given that OP is 4, we can solve the proportion for ON and find its length.

Answer 2

Answer:
`√(14)`

Step-by-step explanation: