The graph of y = f(x) is the solid black graph below. Which function represents the dotted graph?
1 answer:
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First notice that the triangle with sides 
and the triangle with sides 
are similar. This is true because the angle between sides 
in the smaller triangle is clearly 
, while the angle between sides 
in the larger triangle is clearly 
. So the triangles are similar with sides corresponding to 
, respectively.
Now both triangles are
, which means there's a convenient ratio between its sides. If the length of the shortest leg is 
, then the length of the longer leg is 
and the hypotenuse has length 
.
Since
is the shortest leg in the larger triangle, it follows that 
, so 
Now both triangles are
Since
Answer: 33 ft².
Step-by-step explanation:
1. As you can see in the figure attached, the trapezoid is formed by a rectangle and two equal right triangles. The base of each triangle is 4 feet and you know the lenght of the hypotenuse AD, therefore, you can calculate the height by applying the Pythagorean Theorem:
2. Now, you can calculate the area with the following formula:
Where <em>B</em> is the longer base,<em> b</em> is the shorter base and <em>h</em> is the height.
Then:
