If the length L of a rectangle is 3 meters more than twice its width and its perimeter is 300 meters, which of the following equations could be used to find L?

1 Answer
Aug 3, 2015

Answer:

#L="101 m"#
#w = "49 m"#

Explanation:

You have two equations to work with, the equation that describes the perimeter of the rectangle and the equation that describes the relationship between its length, #L#, and width, #w#.

The perimeter of a reactangle is always equal to

#P = 2 *(L + w)#

In your case, you have

#2(L+w) = 300#

Now, you know that if you double the width and add three meters to the result, you get #L#. This means that

#L = 2 * w + 3#

You now have a system of two equations

#{(2L + 2w = 300), (L = 2w + 3) :}#

Use the value of #L# from the second equation to replace #L# in the first equation. This will get you

#L = 2w+3#

#2 * (2w + 3) + 2w = 300#

#4w + 6 + 2w = 300#

#6w = 294 => w= color(green)(49)#

This means that #L# is equal to

#L = 2 * w + 3#

#L = 2 * 49 + 3 = color(green)(101)#

The rectangle will thus be 49 m wide and 101 m long.