Answer:
The length of the sides are 11.5 + 11.5 + 11 + 11.
Step-by-step explanation:
Because this is the perimeter of a quadrilateral, there have to be four numbers that you add together. Since you cannot divide 45 by four evenly, you have to look at the remainder of the quotient that you get from 45/4. The answer is 11 r1. Now you can take the remainder and split it in half to get 11.5. You have to use that number for two of the sides because this is a quadrilateral. When you add these two sides up, you get 23.0 or just 23. However, you need four sides, so you now take the other two 11s from the division and add those together to get 22. 22 + 23= 45.
<h3>
Answer: A. 18*sqrt(3)</h3>
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Explanation:
We'll need the tangent rule
tan(angle) = opposite/adjacent
tan(R) = TH/HR
tan(30) = TH/54
sqrt(3)/3 = TH/54 ... use the unit circle
54*sqrt(3)/3 = TH .... multiply both sides by 54
(54/3)*sqrt(3) = TH
18*sqrt(3) = TH
TH = 18*sqrt(3) which points to <u>choice A</u> as the final answer
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An alternative method:
Triangle THR is a 30-60-90 triangle.
Let x be the measure of side TH. This side is opposite the smallest angle R = 30, so we consider this the short leg.
The hypotenuse is twice as long as x, so TR = 2x. This only applies to 30-60-90 triangles.
Now use the pythagorean theorem
a^2 + b^2 = c^2
(TH)^2 + (HR)^2 = (TR)^2
(x)^2 + (54)^2 = (2x)^2
x^2 + 2916 = 4x^2
2916 = 4x^2 - x^2
3x^2 = 2916
x^2 = 2916/3
x^2 = 972
x = sqrt(972)
x = sqrt(324*3)
x = sqrt(324)*sqrt(3)
x = 18*sqrt(3) which is the length of TH.
A slightly similar idea is to use the fact that if y is the long leg and x is the short leg, then y = x*sqrt(3). Plug in y = 54 and isolate x and you should get x = 18*sqrt(3). Again, this trick only works for 30-60-90 triangles.
Hello,
may i know which digits are underlined
I believe that it is 2x^2+1x-2