An architect designs a rectangular flower garden such that the width is exactly two thirds of the length of 220 feet of an antique picket fencing are to be used

Answer 1

So antique fencing will go around the outside edges of the garden. If the garden is a rectangle, the there are two lengths and two widths, so the distance around the outside (the perimeter) is 2L + 2W

They tell us that we have 220 feet of fencing, so that goes around the perimeter, so 220 = 2L + 2W

If we divide everything by 2, it will make this more manageable: 110 = L + W

Now, we are also told that "the width is exactly two-thirds of the length"

The word "IS" translates to "=" in math. So "the width is" becomes "W = "

and the "two-thirds of the length" is exactly what it says " (2/3) L "

Putting these together, we get W = (2/3)L

and we will substitute this W into the equation above (110 = L + W) so 110 = L + (2/3)L

Adding fractions we need a "common denominator", s

o if we replace L with (3/3) L (that is 1*L, with 1 written 3/3) now we can add (3/3)L + (2/3)L = (5/3)L

Our equation is now 110 = (5/3)L

Now we multiply by the reciprocal on the right side (3/5) to both sides

(3/5)(110) = (3/5)(5/3)L

66 = L

And W = (2/3)L = (2/3)(66) = 44 = W

The dimensions of the rectangular flower garden are 66 ft x 44 ft