SOLUTION: In this problem, they give me the diagram of a rectangle with a diagonal dividing it in two triangles. Each corner is labeled with A, B, C, and D. The perimeter of a rectangle

Algebra ->  Matrices-and-determiminant -> SOLUTION: In this problem, they give me the diagram of a rectangle with a diagonal dividing it in two triangles. Each corner is labeled with A, B, C, and D. The perimeter of a rectangle       Log On


   

Question 174673This question is from textbook Prentic Hall Mathematics Algebra 2
: In this problem, they give me the diagram of a rectangle with a diagonal dividing it in two triangles. Each corner is labeled with A, B, C, and D.
The perimeter of a rectangle is 28 cm. The perimeter of each of the triangles is 24 cm. The diagonal of the rectangle is 2 cm longer than the longer side of the rectangle.
How do you write a system of three questions in three unknowns?
How do you simplify the system to a system of two equations in two unknowns?
And how can I write an augmented matrix for the system?
This is what I've done so far:
2a+2b=28
a+b+x=24
2+a=?
Thankyou&Happy New Year!! This question is from textbook Prentic Hall Mathematics Algebra 2

Found 2 solutions by Mathtut, stanbon:
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
let L and W be the sides of the rectangle and Z be the diagonal
:
2L+2W=28.....eq 1
L+W+Z=24.....eq 2
L+2=Z........eq 3
:
take Z's value of L+2 from eq 3 and plug it into eq 2
:
L+W+(L+2)=24--->2L+W=22....revised eq 2
:
now we have 2 eq with 2 unknownssystem%282L%2B2W=28%2C2L%2B+W=22%29
:
augmented matrix%28matrix%282%2C3%2C2%2C2%2C28%2C2%2C1%2C22%29%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The perimeter of a rectangle is 28 cm. The perimeter of each of the triangles is 24 cm. The diagonal of the rectangle is 2 cm longer than the longer side of the rectangle.
Let shorter side be a; let longer side be b: let diagonal be c
Equations:
2a + 2b = 28
a + b + c = 24
c = b + 2
write a system of three questions in three unknowns
---------------
Rearrange the equations:
2a + 2b + 0 = 28
a + b + c = 24
0 + b - c = -2
-----------------------------
simplify to a system of two equations in two unknowns?
let b = c+2
Then you get:
2a + 2(c+2) + 0 = 28
a + c+2 + c = 24
----
Rearrange:
2a + 2c = 24
a + 2c = -2
----
write an augmented matrix for the system?

2...2..|..24
1...2..|..-2
=====================
Cheers,
Stan H.