Question

Rahul has a farm he wishes to fence. The farm is the pentagon ABCDE. 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.

Answer 1

AE = 120.83 m DE= 148.66 m

The perimeter of the pentagon is 699.49 meters

Sketch attached.

Explanation: First we have to imagine the shape of the pentagon. In order to satisfy the requirement "that E is 50 m from the side AB and 30 m from the side BC," this must be a concave pentagon.

To determine the lengths of sides AE and DE, subtract the given distances of E from the lines, and use those values in the Pythagorean Theorem.

AE: c² = 110² + 50² c=√14600 AE = 120.830 m

DE: c² = 100² + 110² c = √22100 DE = 148.661 m

Add those lengths and the remaining sides of the 140m × 150m rectangle to calculate the perimeter.

280+150+120.83+148.66= 699.49