Perimeter = 27 + 9*sqrt(3), Approximately 42.58845727
Area = 40.5*sqrt(3). Approximately 70.14805771
Since all triangles have a total of 180 degrees and we've been given 2 of those angles, the remaining angle is 180 - 90 - 60 = 30 degrees. So we have a 30,60,90 degree right triangle. Drawing the triangle and assigning the proper angle to each vertex shows that AK is the short leg of the triangle. And since it's a 30,60,90 triangle, the hypotenuse is AL and it will be twice the length of AK, so it's 18. And finally, we can use the Pythagorean theorem to calculate the length of KL. So
KL = sqrt(18^2 - 9^2) = sqrt(324 - 81) = sqrt(243) = sqrt(81*3) = 9*sqrt(3)
So the perimeter is
P = 9 + 18 + 9*sqrt(3) = 27 + 9*sqrt(3). Which is approximately 42.58845727
The area is base times height divided by 2. And we have a base of 9 and a height of 9*sqrt(3). So
A = 9 * 9*sqrt(3)/2 = 81*sqrt(3)/2 = 40.5*sqrt(3). Which is approximately 70.14805771
Answer: A = (b²-5b)/2
Step-by-step explanation:
Hi, to answer this question we have to analyze the information given:
Base =b
Height = h = b-5 (the height is 5 units shorter than the base)
Since:
Area of a triangle (A)= (base x height) ÷ 2
Replacing with the values given:
A = [b (b-5)] ÷2
A = (b²-5b)/2
Feel free to ask for more if needed or if you did not understand something.
Answer:
19.50
Step-by-step explanation:
just trust me
I'll solve 21, and you then should be able to solve the rest on your own!
Since ADC is 135, that means that that whole angle is 135 degrees. In addition, since angles ADB and BDC add up to ADC, we get ADB+BDC=ADC=135=11x+9+7x=18x+9. Subtracting 9 from both sides, we get 126=18x. Dividing both sides by 18, we get x=7. Plugging that into 11x+9=BDC, we get 11*7+9=77+9=86
Angles XQL and MQR are congruent because they are vertical angles. So
209 - 13 <em>b</em> = 146 - 4 <em>b</em>
Solve for <em>b</em> :
209 - 13 <em>b</em> = 146 - 4 <em>b</em>
209 - 146 = 13 <em>b</em> - 4<em> b</em>
63 = 9 <em>b</em>
<em>b</em> = 63/9 = 7
Then the measure of angle XQL is
(209 - 13*7)º = 118º
