A surveyor wishes to lay out a square region with each sidehaving length L. However, because of a measurement error,he instead lays out a rectangle in which the north–south sides both have length X and the east–west sides both have lengthY. Suppose that X and Y are independent and that each isuniformly distributed on the interval [L 2 A, L 1 A] (where0 , A , L). What is the expected area of the resultingrectangle?

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter8: Areas Of Polygons And Circles
Section8.2: Perimeter And Area Of Polygons
Problem 34E: The farmer in Exercise 33 has decided to take the fencing purchased and use it to enclose the...
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A surveyor wishes to lay out a square region with each side
having length L. However, because of a measurement error,
he instead lays out a rectangle in which the north–south sides both have length X and the east–west sides both have length
Y. Suppose that X and Y are independent and that each is
uniformly distributed on the interval [L 2 A, L 1 A] (where
0 , A , L). What is the expected area of the resulting
rectangle?

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