Archaeologists discovered that the 18th century garden of the Charles Carroll House in Annapolis Maryland was a right triangle. The long leg of the triangle was

Question

Archaeologists discovered that the 18th century garden of the Charles Carroll House in Annapolis Maryland was a right triangle. The long leg of the triangle was formed by a 400ft. long sea wall. The hypotenuse of the triangle was 200 ft. longer than the shorter leg. What were the garden dimensions?

Answer 1

You have a right triangle;

Leg 1:  400

Leg 2:  x

Hypotenuse:  x + 200

 

From Pythagorean Theorem:

 

(x+200)² = x² + 400²

x² + 400x + 40000 = x² + 160000

400x - 120,000 = 0

x - 300 = 0

x = 300

 

The short leg is 300 ft

The hypotenuse is 500 ft

Long leg, as given, is 400 ft