PUNCHLINE-Algebra-8.9 answer key

Question

The perimeter of a rectangle is 42. The perimeter of a triangle is 36. Find the values of x and y

Answer 1

Hi Torry!

This must be guess the figure day -- this

is the second one I've done today with no figure. :-D

Ok, so I'm assuming both figures are using the

variables x and y as sides in some way.

The dimensions of the rectangle are x by y

(assuming once again the sides are different).

The perimeter is then x+y+x+y or 2x+2y.

We are given the perimeter of the rectangle is 42,

so 2x + 2y = 42 is one equation.

For the triangle, we have 4 possibilities:

1. All the sides of length x
2. All the sides of length y
3. 2 of the sides length x, one length y
4. 2 of the sides length y, one length x

For possibility 1, the perimeter of the triangle is

x+x+x = 3x. We are given the perimeter is 36,

so 3x = 36. Solving this for x we get x = 12.

Plugging this into the rectangle equation,

2(12) + 2y = 42

24 + 2y = 42

2y=18

y=9

So here is one possibility 1: x=12, y=9

For possibility 2, the perimeter of the triangle

is y+y+y = 3y. We are given the perimeter is 36,

so 3y=36. Solving this for y, we get y=12.

Plugging this into the rectangle equation:

2x + 2(12) = 42

2x + 24 = 42

2x = 18

x = 9

Here is possibility 2: x=9, y=12

For possibility 3, the perimeter of the

triangle is x+x+y or 2x+y. We are given

the perimeter is 36, so 2x + y = 36.

Use the rectangle equation along with

this to figure this system of equations.

2x + y = 36

-(2x + 2y = 42) subtract the second from the first

-----------------

-y = -6 or y = 6

Plug this into the 2x+y=36 equation to find x.

2x + 6 = 36

2x = 30

x = 15

Here is possibility 3: x=15, y=6

For possibility 4, the perimeter of the

triangle is x+y+y or x+2y. We are given

the perimeter is 36, so x + 2y = 36.

Use the rectangle equation along with

this to figure this system of equations.

x + 2y = 36

-(2x + 2y = 42) Subtract the 2 equations

-x = -6 or x = 6

Plug this into the x + 2y = 36 equation to find y

6 + 2y = 36

2y = 30

y = 15

Here is possibility 4: x =6, y=15

So, one of these possibilities should be your

answer. I can't tell you which one though

without seeing the figure!

Answer 2

This is not answerable.