In rectangle PQRS, PR = 11x – 20and QS = x + 160.
1 answer:
Answer:
![\large \boxed{1.\, x = 18; 2.\, 178}](https://tex.z-dn.net/?f=%5Clarge%20%5Cboxed%7B1.%5C%2C%20x%20%3D%2018%3B%202.%5C%2C%20178%7D)
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}}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcll%7D11x%20-%2020%20%26%20%3D%20%26%20x%20%2B%20160%20%26%20%5C%5C11x%20%26%3D%20%26%20x%20%2B%20180%20%26%20%5Ctext%7BAdded%2020%20to%20each%20side%7D%5C%5C10x%20%26%20%3D%20%26%20180%20%26%20%5Ctext%7BSubtracted%20x%20from%20each%20side%7D%5C%5Cx%26%20%3D%20%26%20%5Cmathbf%7B18%7D%20%26%5Ctext%7BDivided%20each%20side%20by%2010%7D%5C%5C%5Cend%7Barray%7D%5C%5C%5Clarge%20%5Cboxed%7B%5Cmathbf%7Bx%20%3D%2018%7D%7D)
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.
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