Please answer 100 pt
2 answers:
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To solve this problem, we need to first find the dimensions of the side of the blue and purple squares.
We're given that the purple (smaller) square has a side length of x inches.
We are also given that the blue band has a width of 5 inches.
Since the blue band surrounds the purple square on both sides, the length of the blue square is x+2(5)=x+10 inches.
The net area of the band is therefore the difference of the area of the blue square and the purple square, namely take out the area of the purple square from the blue.
Therefore
Area of band
[recall 
or 20(x+5) if you wish.
We're given that the purple (smaller) square has a side length of x inches.
We are also given that the blue band has a width of 5 inches.
Since the blue band surrounds the purple square on both sides, the length of the blue square is x+2(5)=x+10 inches.
The net area of the band is therefore the difference of the area of the blue square and the purple square, namely take out the area of the purple square from the blue.
Therefore
Area of band
Hi!
Let's first expand the cotangent of theta.
You'll probably know that tangent will be "y/x", or , and cotangent is the reciprocal of this, meaning that it is "x/y" or
.
That means that we are now given this equation.
That'll multiply to:
We'll want a common denominator to add by multiplying to both top and bottom of the second term:
Pythagorean Identity states that , so substitute that in:
Which simplifies to:
Hope this helps!