|
Question 1180912: A pool is in the shape of a regular polygon. Each interior angle of the pool is four times larger than its exterior angle. If the length of each side of the pool is 1.8m, determine the perimeter of the pool.
Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A pool is in the shape of a regular polygon.
Each interior angle of the pool is four times larger than its exterior angle.
If the length of each side of the pool is 1.8m, determine the perimeter of the pool.
:
Int Angle = (180n-360)/n, where n = no. of sides
Ext Angle = 360/n
"Each interior angle of the pool is four times larger than its exterior angle."
(180n-360/n = 4(360/n)
multiply both sides by n
180n - 360 = 1440
180n = 1440 + 360
180n = 1800
n = 1800/180
n = 10
10 sides
Find the perimeter
10 * 1.8 = 18 meters
Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
Here is an easier way to get the same answer as the other tutor....
"Each interior angle of the pool is four times larger than its exterior angle."
So let the exterior and interior angle measures be x and 4x.
The sum of the interior and exterior angle measures is 180 degrees:
x+4x=180
5x=180
x=36
The measure of the exterior angle is 36 degrees.
The number of sides on the pool is 360/36=10
The perimeter of the pool is 10(1.8m) = 18m.
------------------------------------------------------------------------
While that is almost certainly the intended answer to the problem, that answer is wrong.
The problem is that the statement quoted above does NOT mean what nearly everybody thinks it means.
If a number is x, then the number four times AS LARGE AS x is 4x.
But if a number is x, then the number four times LARGER THAN x is x, plus x 4 MORE times, which is x+4x=5x.
So the correct answer to the problem as stated is not 18m; the number of sides of the pool is not 10.
Interpreting the given information correctly, the measures of the interior and exterior angles are x and 5x:
x+5x=180
6x=180
x=30
The measure of the exterior angle is 30 degrees.
The number of sides of the pool is 360/30=12
The perimeter of the pool is 12(1.8m)=21.6m
Unfortunately, in everyday usage, the phrases "4 times as large as" and "4 times larger than" are nearly always carelessly used to mean the same thing. But grammatically and mathematically they mean different things.
Because of the standard misuse of the phrase "n times larger than", that phrase, or any similar phrase, should NEVER be used in the statement of a math problem.
|
|
|
| |
