Results 1 to 6 of 6

- Feb 13th 2008, 05:55 AM #1

- Joined
- Jan 2008
- Posts
- 10

## Can someone help me on this?

Hi! We just started doing a new lesson at mathes and I did pretty well for most homework we got, but I didn't get the three last questions we got here, so I'd love if someone would help me!

1-ABC is a right triangle (with A=90°). AB is 27 ft. The perimeter of this triangle is 108 feet. What is the length of AC and AB?

2-If x-y=-3 and x²-y²=6, what is x and y?

3-If x+y=20 and x²-y²=40, what is x and y?

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?

Thanks in advance y'all!

- Feb 13th 2008, 06:03 AM #2

- Feb 13th 2008, 06:05 AM #3

- Feb 13th 2008, 06:09 AM #4
Call the original length of the garden x and the original width y, and call A = xy the area of the original garden.

Then

So

Since the new shape is a square we also know that

So solve this last equation for y and put the result into your area equation.

I get x = 23 and y = 14.

-Dan

- Feb 13th 2008, 08:20 AM #5

- Joined
- May 2006
- From
- Lexington, MA (USA)
- Posts
- 12,028
- Thanks
- 846

Hello, Catherine!

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

1) is a right triangle (with ). . is 27 ft.

The perimeter of this triangle is 108 feet.

What is the length of and ?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

2) If and , find and

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?

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.

- Feb 14th 2008, 09:13 AM #6

- Joined
- Jan 2008
- Posts
- 10