Quadrilateral LMNO is similar to quadrilateral PQRS. Find the measure of side SP. Round your answer to the nearest tenth if necessary.

Answer 1

To find the measure of side SP, we can set up a proportion using the corresponding sides of the two similar quadrilaterals.

Let's denote the lengths of sides LM, NO, SP, and QR as x, y, a, and b respectively.

From the given information, we know that LMNO is similar to PQRS, so we can set up the following proportion:

SP/QR = NO/RS

Substitute the values:

a/b = y/x

Now we know that sides NO and RS measure 12 units and 15 units respectively. We can substitute these values into the proportion:

a/15 = 12/x

Cross multiply:

ax = 12*15
ax = 180
a = 180/x

Now we need to find the measure of side SP, so we substitute the given length of NO into the equation:

12 = 180/x
x = 180/12
x = 15

Therefore, the measure of side SP is equal to 15 units.