Question

The quadrilaterals ABCD and PQRS are similar. Find the length X of SP.

Answer 1

To determine the length of 'X' for similar quadrilaterals ABCD and PQRS, we would utilize the properties of similar figures and set up a proportion using the known side lengths to solve for the unknown length 'X' of SP.

Step-by-step explanation:

The question appears to be mixed with different contexts that do not directly relate to finding the length of 'SP' in similar quadrilaterals ABCD and PQRS as initially stated. However, understanding the properties of similar figures in geometry can help solve similar problems. In the context of similar quadrilaterals, if ABCD and PQRS are similar, the corresponding sides are proportional. Suppose we knew the lengths of the sides of ABCD, we could set up a proportion to find the unknown length 'X' of SP by using the ratio of corresponding sides.

Similar Figures

For similar figures:

• If two quadrilaterals are similar, then their corresponding angles are equal, and the ratios of the lengths of their corresponding sides are equal.
• To determine the unknown side, we could use the proportion AB/CD = PQ/RS given 'AB' and 'CD' for the first quadrilateral and 'PQ' for the second.
• Find the length of 'X' would involve substituting the known values into our proportion and solving for 'X'.

Answer 2

`x = 3.6`

Step-by-step explanation:

Since Quadrilateral ABCD ~ PQRS, therefore:

`(AB)/(PQ) = (BC)/(QR) = (CD)/(RS) = (DA)/(SP)`

Let's find the value of x by using the ratio of two corresponding sides of both quadrilaterals. Let's use:

`(CD)/(RS) = (DA)/(SP)`

CD = 5

RS = 4.5

DA = 4

SP = x

`(5)/(4.5) = (4)/(x)`

Cross multiply

`5*x = 4.5*4`

`5x = 18`

Divide both sides by 5

`x = (18)/(5)`

`x = 3.6`