perimeter of a triangle and quadrilateral
- Thread starter Bucky49
- Start date
Dr.Peterson
Elite Member
- Joined
- Nov 12, 2017
- Messages
- 16,088
Please give us a clue as to what sort of help you need, as requested here:
Can you express the condition that the perimeters both equal 27, as a pair of equations in x and y? Or can you determine y, and then x?
READ BEFORE POSTING
Welcome to FreeMathHelp.com! Please take the time to read the following before you make your first post. It will help you to get your math questions answered promptly and in the most helpful manner. A summary is available here, but please read the complete guidelines below at your earliest...
www.freemathhelp.com
Can you express the condition that the perimeters both equal 27, as a pair of equations in x and y? Or can you determine y, and then x?
HallsofIvy
Elite Member
- Joined
- Jan 27, 2012
- Messages
- 7,763
Do you know what "perimeter" means? If do then it should be easy to write the perimeter of the quadrilateral in terms of x and y and the perimeter of the triangle in terms of y only. Set them both equal to 27 and you have two equations to solve for x and y.
ausmathgenius420
New member
- Joined
- Aug 5, 2021
- Messages
- 44
We want to find the values of x and y (so that we can find their sum).
To do this we will need simultaneous equations
We know the perimeter of region a and the perimeter of region be are both equal to 27.
Region a has 4 sides (x,x,x,y) therefore:
[math]27=3x+y[/math]
Region b has 3 sides (y,y,y) therefore:
[math]27=3y[/math]
The substitution method is the easiest way to go about solving this. I would rearrange equation 1 in terms of y so:
[math]y=27-3x[/math]
The rest is simple algebra. If we know [imath]y=27-3x[/imath] and [imath]27=3y[/imath] then:
[math]27=3(27-3x)[/math]
Use this same method to solve for y then add both values.
To do this we will need simultaneous equations
We know the perimeter of region a and the perimeter of region be are both equal to 27.
Region a has 4 sides (x,x,x,y) therefore:
[math]27=3x+y[/math]
Region b has 3 sides (y,y,y) therefore:
[math]27=3y[/math]
The substitution method is the easiest way to go about solving this. I would rearrange equation 1 in terms of y so:
[math]y=27-3x[/math]
The rest is simple algebra. If we know [imath]y=27-3x[/imath] and [imath]27=3y[/imath] then:
[math]27=3(27-3x)[/math]
Use this same method to solve for y then add both values.
Otis
Elite Member
- Joined
- Apr 22, 2015
- Messages
- 4,414
Hi ausmathgenius420. I agree that one ought to solve a system of two equations, if that's what the class is studying. Otherwise, in the absence of specific instruction (eg: question in some general placement test), we're free to determine the answer however we choose.
For example, I'd seen that y is 9 just by looking at the diagram (as could anyone who understands the meaning of the multiplication table). Likewise, after having mentally removed side y from the quadralateral, it was clear that x is one-third of what remained. So, a person could do 9+18/3 in their head and answer without ever writing symbols x or y. (That line of reasoning jives with Dr. Peterson's second suggestion.)
