http://www.gulname.com/sea-coral-round/
can you please help me with this (10 pts)!!?
About 6,565 square miles of the Coral Sea is protected by the government. Imagine a large rectangle with an area of 6,565 square miles. The length of the rectangle is four times the width of the rectangle. What is the length of a diagonal on such a rectangle? Round to the nearest whole number.
A.) 151 miles
B.) 174 miles
C.) 167 miles
D.) 189 miles
OK. You have to use algebra for this one.
L=Length
W=Width
W=y
L=4y
Area=A
2= Squared
A = y x 4y
A= 4y2
To get y you have to follow these steps:
6565 / 5 = 1641
Which also equals y2
Square root 1641 = 40.51
y=40.51
4y=162
Now we cut the rectangle in half and we have a triangle. To find the side we don't have (the diagonal) we use Pythagoras's theorem.
In Pythagoras's theorem the HYPOTENUSE = the diagonal in your question.
Pythagoras's theorem = The sum of the two sides that are NOT the hypotenuse squared is equal to the hypotenuse squared.
So...
40.51 squared = 1641
162 squared = 26244
Therefore: 1641 + 26244 = The hypotenuse squared
1641 + 26244 = 27885
The square root of 27885 = 166.9 (or 167)
Therefore the answer is:
C) 167 miles
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