Question

In rectangle PQRS, PR = 11x – 20and QS = x + 160.

Answer 1

Answer:

$\large \boxed{1.\, x = 18; 2.\, 178}$

Step-by-step explanation:

1. Value of x

The diagonals of a rectangle are equal, so

PR = QS

$\begin{array}{rcll}11x - 20 & = & x + 160 & \\11x &= & x + 180 & \text{Added 20 to each side}\\10x & = & 180 & \text{Subtracted x from each side}\\x& = & \mathbf{18} &\text{Divided each side by 10}\\\end{array}\\\large \boxed{\mathbf{x = 18}}$

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.