Answer:
Explanation:
You want the values of x and PS for the trapezoid in the figure, given that its perimeter is 228 units.
Symmetry
The trapezoid is shown as an isosceles trapezoid, so PS = RQ. The Triangle RTQ will be repeated on the left side, meaning there is a point T' below point S such that T'P = 4 and T'T = SR = 4x+1.
Perimeter
The perimeter is the sum of side lengths. Working clockwise from the upper left corner this is ...
perimeter = (4x+1) +(2x -3) +4 +(4x +1) +4 +(2x -3) = 12x +4
Solution
Solving for x, we find ...
12x +4 = 228
12x = 224
x = 224/12
x = 18 2/3
And PS is ...
PS = RQ = 2x -3 = 2(18 2/3) -3 = 37 1/3 -3
PS = 34 1/3
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