Problem of the Week
Problem
B
Seeking
Parts Unknown...

Sylvana and Roberto divide a \(40\)
m by \(75\) m rectangular lot to form
two yards, as shown in the diagram below.

A rectangle placed horizontally with the top and bottom sides of the rectangle greater in length than the left and right sides. A diagonal line slants down and to the left from the top side to the bottom side of the rectangle, dividing the rectangle into two trapezoids. The trapezoid on the left is labelled Sylvana’s yard and the trapezoid on the right is labelled Roberto’s yard. The top side of Sylvana’s yard has length \(60\) m, the bottom side has length \(30\) m, and the left side has length \(40\) m. The top side of Roberto’s yard has length \(x\) and the bottom side has length \(y\).

The area of Roberto’s yard is \(40\%\) of the total area of the two
properties.

What are the values of \(x\) and
\(y\), the missing dimensions of
Roberto’s yard?