6 1/5 x 15 1/5 = ???
2 answers:
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Answer: C. 17.5 feet
Step-by-step explanation:
The attached photo shows the triangle ABC formed by the ladder and the wall. It is a right angle triangle because one of its angles is 90 degrees. The ladder is the hypotenuse of the triangle. To determine the height of the wall, we would find BC by applying Pythagoras theorem
Hypotenuse^2 = opposite ^2 + adjacent^2
18^2 + 4.5^2 + BC^2
BC^2 = 324 - 20.25 = 303.75
BC = √303.75 = 17.5 feet.
A rectangle with dimensions and
has perimeter 20 if
and we can deduce
So, the dimensions of the rectangle must be and
, where x ranges from 0 to 10 (both extremes are excluded, otherwise you'd have a degenerate rectangle, which is actually a segment).
So, all the possible areas are given by the product of the dimensions, i.e.
The function represents a parabola, facing downwards, and thus it admits a maximum, which is its vertex.
In particular, the vertex of this parabola is given by
And it yields an area of
(a) So, she can frame a maximum area of 25 squared yards.
(b)The dimensions of the rectangle with greatest area are and
, so it's actually a square.
This is a well known theorem: if you fix the perimeter, the rectangle with the largest area is the square yielding that perimeter.
(c) If we increase both dimensions by 2 yards, our 5x5 square would become a 7x7 square...
(d) ...and the new area would be squared yards. So, the new area is
squared yeards more than the old one.