SOLUTION: a rectangle with a perimeter of 102 inches is half as wide as it is long determine the length of this rectangle in inches

Algebra ->  Rectangles -> SOLUTION: a rectangle with a perimeter of 102 inches is half as wide as it is long determine the length of this rectangle in inches      Log On


   

Question 620108: a rectangle with a perimeter of 102 inches is half as wide as it is long determine the length of this rectangle in inches
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--
.
STEP I: Choose variables
.
Let W be the width of the rectangle.
Let L be the length.
.
STEP II: Write equations to model the situation.
.
The formula for the perimeter of a rectangle is P = 2W+2L, so
102=2W%2B2L
51=W%2BL
.
In algebra, "half as wide as it is long" can be written as
W=%281%2F2%29%2AL
.
Note: It's easy to confuse the words with the algebra. Once you have your equation test it with a few values. For example, "3 is half as wide as 6, and 3=(1/2)*6.
.
STEP III: Solve your system of equations.
Substitute(1/2)*L for W in the first equation.
51=W%2BL
51+=+%281%2F2%29%2AL%2BL
.
Simplify.
51=%283%2F2%29L
L=%282%2F3%29%2851%29=34
.
The length of the rectangle is 34 inches.
.
STEP IV: Check your work.
Since the rectangle is half as wide as it is long, the width must be 17. Thus the perimeter is 2(17)+2(34)=34+68=102. Check!
.
Hope this helps. Feel free to email if you still have questions about this.
.
Ms.Figgy
math.in.the.vortex@gmail.com