Question 98824
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.