Question

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

Answer 1

Answer:

$x = 3.6$

Step-by-step explanation:

Since Quadrilateral ABCD ~ PQRS, therefore:

$\frac{AB}{PQ} = \frac{BC}{QR} = \frac{CD}{RS} = \frac{DA}{SP}$

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

$\frac{CD}{RS} = \frac{DA}{SP}$

CD = 5

RS = 4.5

DA = 4

SP = x

$\frac{5}{4.5} = \frac{4}{x}$

Cross multiply

$5*x = 4.5*4$

$5x = 18$

Divide both sides by 5

$x = \frac{18}{5}$

$x = 3.6$