Answer:
[tex]\large \boxed{1.\, x = 18; 2.\, 178}[/tex]
Step-by-step explanation:
1. Value of x
The diagonals of a rectangle are equal, so
PR = QS
[tex]\begin{array}{rcll}11x - 20 & = & x + 160 & \\11x &= & x + 180 & \text{Added 20 to each side}\\10x & = & 180 & \text{Subtracted x from each side}\\x& = & \mathbf{18} &\text{Divided each side by 10}\\\end{array}\\\large \boxed{\mathbf{x = 18}}[/tex]
2. Length of each diagonal
PR = 11x - 20 = 11×18 - 20 = 198 - 20 = 178
QS = x + 160 = 18 + 160 = 178
The length of each diagonal is 178.
