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Problem of the Week

Problem C

Around the Farm

Rahul has a farm he wishes to fence. The farm is the pentagon \(ABCDE\) shown below. He knows that \(ABCD\) is a 140 m by 150 m rectangle. He also knows that \(E\) is 50 m from the side \(AB\) and 30 m from the side \(BC\).
Determine the length of \(AE\), the length of \(DE\), and the perimeter of pentagon \(ABCDE\).

Side B C has length 140 metres and side C D has length 150 metres. Point E is in the interior of rectangle A B C D. A line is drawn perpendicular to side B C through E indicating the distance from B C to E and similarly for the distance from A B to E.

NOTE: The Pythagorean Theorem states, “In a right-angled triangle, the square of the length of hypotenuse (the side opposite the right angle) equals the sum of the squares of the lengths of the other two sides”.
In the following right triangle, \(p^2=r^2+q^2\).

A right-angled triangle with hypotenuse of length p and remaining sides of length r and length q.

Theme: Geometry