SOLUTION: A rectangle with a length of 3 and width of ("x- 1")has an area of "m" square units and the perimeter of "2m" units. What is the value of "x"?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A rectangle with a length of 3 and width of ("x- 1")has an area of "m" square units and the perimeter of "2m" units. What is the value of "x"?      Log On


   

Question 99905: A rectangle with a length of 3 and width of ("x- 1")has an area of "m" square units and the perimeter of "2m" units. What is the value of "x"?
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
A=L*W
A=3(x-1)=3x-3=m
P=2(L+W)=2(3+x-1)=2(x+2)=2x+4=2m
.
3x-3=m
2x+4=2m
.
3x-m=3
2x-2m=-4
.
multiply -2 times the top equation:
-6x+2m=-6
2x-2m=-4
----------add
-4x=-10
x=2.5 Ans.
replace 2.5 for x in the 1st equation: m=3*2.5-3=7.5-3=4.5
m=4.5
Check:
3*(2.5-1)=4.5 true
2(3+2.5-1)=2*4.5...2*4.5=2*4.5 true
Ed