The measure of side length TP (x) in pentagon PQRST is 2.4.
The figure in the image are two similar pentagons.
Pentagon JKLMN is similar to pentagon PQRST.
From the image, pentagon JKLMN;
Side JK = 5
Side KL = 4
Side LM = 2
Side MN = 2
Side NJ = 3
In pentagon PQRST:
Side PQ = 4
Side QR = 3.2
Side RS = 1.6
Side ST = 1.6
Side TP = x
To solve for the measure of side length TP, we use proportion.
Since the two pentagon are similar:
Side JK / Side NJ = Side PQ / Side TP
Plug in the values:
5/3 = 4/x
Cross multiply:
5x = 3 × 4
5x = 12
x = 12/5
x = 2.4
Therefore, the value of x is 2.4.