Question 98824: The length of a a rectangle is twice as long as the width. The perimeter of the rectangle is 72 in. What are the length and width of this rectangle.
Found 2 solutions by doukungfoo, anjali_yamini:
Answer by doukungfoo(195)   (Show Source):
You can put this solution on YOUR website! Ok first lets make some statements about a rectangle.
The perimeter of a rectangle is equal to the sum of all its sides.
Both sides that make up a rectangles length will always be equal
and both sides that make up a reactangles width will always be equal.
Now we can write and equation to express the perimeter of the rectangle, but first lets define some variables. length = a and width = b The perimeter is given to be 72 inches. So since we know the perimeter of a rectangle is equal to the sum of all its sides we can say that:
a + a + b + b = 72
then simplify it to
2a + 2b = 72
Now the problem also tells us that the length is equal to twice the width. That can be expressed as:
a = 2b
Now since length = a and a = 2b we can replace the a in 2a + 2b = 72 with 2b
so now you have this:
2(2b) + 2b = 72
Since there is now only one variable we can solve the equation for b
first multiply 2 times 2b
4b + 2b = 72
then combine like terms
6b = 72
now divide both sides of the equal sign by 6
6b/6 = 72/6
b = 12
Now that we have solve for b we can plug that value into our original equation
2a + 2b = 72
replace b with 12
2a + 2(12) = 72
multiply 2 times 12
2a + 24 = 72
subtract 24 from both sides of equal sign
2a = 48
divide both sides of equal sign by 2
a = 24
to check plug both answers into original equation.
also don't forget the answers are in the unit of inches because the perimeter was given as 72 inches.
Answer by anjali_yamini(27)  (Show Source):
You can put this solution on YOUR website!
let :
l= length of the rectangle
w = width of rectangle
p = perimeter of rectangle = 72
we know that perimeter = sum of all the sides
so, p = l+l+w+w =2(l+w)
since length is twice the width,
l= 2w
so, p = 2(2w +w)
so, 72 = 2( 3w)
so, 72/2 = 3w
so, 36 = 3w
so, 36/3 = w
so, 12 =w
so l = 2*12 = 24
thus the length of the rectangle is 24in, and the width is 12in.
check :
p = 2(l+w)
p = 2(12 +24)
p = 2 * 36
p = 72
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