Question

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 rectangles, as shown below.
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 the pentagon
ABCDE.

Answer 1

The diagram of the pentagon is missing, so i have attached it.

Answer:

|AE| = 130 m

|DE| = 150 m

Perimeter of pentagon = 720 m

Explanation:

From the diagram, we can find AE from pythagoras theorem;

|AE| = √(|AA'|² + 50²)

Where AA' is the length from A to the perpendicular angle.

Now, AB = 150, and A'B is parallel to 30 m. Thus, A'B = 30

AA' = AB - A'B = 150 - 30

AA' = 120

Thus;

|AE| = √(120² + 50²)

|AE| = √(14400 + 2500)

|AE| = √16900

|AE| = 130

Similarly,

|DE| = √(|DD'|² + |ED'|²)

ED' = BC - 50

ED' = 140 - 50

ED' = 90

Also, DD' is parallel to AA' and is = 120

Thus;

|DE| = √(120² + 90²)

|DE| = √22500

|DE| = 150

Perimeter of pentagon = 150 + 130 + 150 + 150 + 140 = 720