How many 6-letter words can be made from the letters WASTEFUL if repetition of letters is allowed?
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I found an image that corresponds to the above question.
The shape was a rectangle. Its width is 7 units, its length is x.
The shaded area of the rectangle forms a trapezoid.
Area of a trapezoid = [(a+b)/2] * h
63 sq. units = (7+x)/2 * 7
63/7 = (7+x)/2
9 = (7+x)/2
9*2 = 7 + x
18 = 7 + x
18 - 7 = x
11 = x
The value of x is 11 units. It is the length of the rectangle.
Area of the trapezoid = (a+b)/2 * h
63 = (7+11)/2 * 7
63 = 18/2 * 7
63 = 9 * 7
63 = 63
The shape was a rectangle. Its width is 7 units, its length is x.
The shaded area of the rectangle forms a trapezoid.
Area of a trapezoid = [(a+b)/2] * h
63 sq. units = (7+x)/2 * 7
63/7 = (7+x)/2
9 = (7+x)/2
9*2 = 7 + x
18 = 7 + x
18 - 7 = x
11 = x
The value of x is 11 units. It is the length of the rectangle.
Area of the trapezoid = (a+b)/2 * h
63 = (7+11)/2 * 7
63 = 18/2 * 7
63 = 9 * 7
63 = 63
Taking the square root of both sides gives two possible cases,
or
Recall that
If and
, we have
so in the equations above, we can write
Then in the first case,
(where is any integer)
and in the second,
Then the solutions that fall in the interval are
