Question

A garden has the form of a right triangle. One leg of the triangle is formed by a 2000-ft long sea wall. The hypotenuse of the triangle is 400 ft longer than the other leg. What are the dimensions of the garden?

Answer 1

`H = 5200` - Hypotenuse

`S_1 = 2000` - Leg 1

`S_2 = 4800` - Leg 2

Explanation:

Represent the dimensions as:

`H = Hypotenuse`

`Other\ Legs = \{S_1,S_2\}`

So, we have:

`S_1 = 2000`

`H = 400 + S_2`

Required

Determine the dimensions

Apply Pythagoras theorem

`H^2 = S_1^2 + S_2^2`

This gives:

`(400 + S_2)^2 = 2000^2 + S_2^2`

Open bracket

`160000 + 800S_2 + S_2^2 = 4000000 + S_2^2`

`160000 + 800S_2 = 4000000`

Collect Like Terms

`800S_2 = 4000000 - 160000`

`800S_2 = 3840000`

Solve for S2

`S_2 = (3840000)/(800)`

`S_2 = 4800`

Recall that:

`H = 400 + S_2`

`H = 400 + 4800`

`H = 5200`

Hence, the dimensions are:

`H = 5200`

`S_1 = 2000`

`S_2 = 4800`