To find the measure of side SP, we need to find the scale factor between the two similar quadrilaterals. Since the quadrilaterals are similar, their corresponding sides are in proportion.
Let's denote the length of LM as x and the length of PQ as y.
From the given information, we can write the proportion:
LM / PQ = NO / RS = MO / PS
Substitute the values we know:
x / y = NO / RS = MO / SP
We are given that NO = 12 and MO = 14. Additionally, we need to find the value of RS, which we can find using the proportion:
LM / PQ = NO / RS
x / y = 12 / RS
Cross-multiply to solve for RS:
x * RS = 12y
RS = 12y / x
Now we can set up a new proportion using the information provided in the question:
x / y = 14 / SP
Cross-multiply to solve for SP:
x * SP = 14y
SP = 14y / x
Now we can substitute the values of NO, MO, x, and y into the equation:
SP = 14 * 12 / x
SP = 168 / x
Since we don't know the exact value of x without additional information, we cannot find the exact measure of side SP.
If you are given the value of x, you can substitute that into the equation to find the measure of side SP.