Rectangle and Square perimeter geometry questions!?!?

Question

I know how to find the permiter of rectangles with the length x width formulas, but this question has degrees and square roots. The first question is rectangle one:

Find the perimeter of rectangle ABCD. (Line DC has 12) and the angle of DAC is 60°. The rectangle has a line through it... How do you solve.

Sqare problem:
Find the perimeter of this square:

(it's a square with a Line through it and the top triangle in the square has 6 times the square root of 3)

Please help if you understand! I can't put it all on there on my iPod.

Answer 1

For the rectangle question, it sounds like this is basically a 30-60-90 triangle. The way that basically works is that the angle measures to side lengths are in the ratio of:



30 : 60 : 90 = x : 2*x : x*sqrt(3)



In this case, you need to find the length of either AC or BD to find the perimeter. This means that angle ADC = 30 degrees.



Since we know the side opposite the 60 degree angle = 12 ==> 2x = 12 ==> x = 6.



Since x is opposite the 30 degree angle, this means that sides AC & BD each have a length of 6. Therefore, the perimeter of the rectangle = 6+6+12+12 = 30.



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For the square problem, it's the exact same idea, except that when a diagonal is drawn in a square, the angle measures of the triangle formed are: 45:45:90. In a 45:45:90 triangle, the ration of angle measures to side lengths is:



45 : 45 : 90 = x : x : x*sqrt(2)



Here's, I'm assuming the diagonal has the length of 6*sqrt(3). The diagonal is the side opposite the 90 degree angle.



So, we have: 6*sqrt(3) = x*sqrt(2)

==> x = 6*sqrt(3)/sqrt(2) = Length of ONE side of the square.



To find the perimeter of the square, the answer is then: 4*(6*sqrt(3)/sqrt(2)) = 24*sqrt(3)/sqrt(2).



Assuming I read the question correctly, I think these are the correct answers.

Answer 2

You need to remember that if you have a 60 degree angle in a right triangle, then the other angle is 30.

If you have a 30-60-90 triangle, then the proportions of the sides is always in the ratio of short side (opposite 30) is 1, the hypotenuse (opposite the 90) is 2 and the middle side opposite the 60 is the square root of 3.

In your first example the hypotenuse (diagonal) is 12, therefore the short side (width of the rectangle) is 6, and the length of the rectangle (middle side of the triangle) is 6(sqrt(3)).

Answer 3

It's trigonometry. For the rectangle based on how you explained it the rectangle is made up of two equal triangles so using triangle DAC you can get thhe perimeter. Using DAC data Tan 60 degrees= 12 divide line AD. Therefore AD= 12/Tan60= 6.93. So sides AD and BC are 6.93 and sides AB and DC are 12 just add them 37.86.

For the square just work out 6 times the sq. Root of 3 which is about 10.4, the value of one side and multiply that by 4 to get the perimeter. Hope i understood the instructions right :) is about 10.4, the value of one side and multiply that by 4 to get the perimeter. Hope i understood the instructions right :)