Hello, Catherine!

The first three can be solved with the same trick . . .

First, make a sketch . . . Code:

C *
| *
| * a
b | *
| *
| *
A * - - - - - - - - * B
27

Let

The perimeter is 108: .

Pythagorus tells us: .

We have a system of equations: .

Equation [1] is: .

Divide by [2]: .

Add [2] and [3]: .

Substitute into [2]: .

Therefore: . feet

Can you see that this system is identical to the system in #1?

We have: .

Substitute into [1]: .

4) A garden has a shape of a rectangle.

If we remove 3 feet from the length of a garden, and add 6 feet to the width,

the garden gets the shape of a square and the total area gains 78 sq ft.

What is the length and width of the garden? I approached this one "backwards".

Let = side of the square garden. .Its area is: ft²

The original garden was 3 feet longer: .

. . and was 6 feet narrower: .

The area of the original garden was: . ft²

The square garden has 78 ft² more than the original garden.

. . .

Therefore, the original garden was ft.