Answer:
Perimeter=42cm
Step-by-step explanation:
It is given that AC is the angle bisector of the trapezoid ABCD which divides the trapezoid into two similar triangles that are △ABC and △ACD.
Now, it is also given that AB=9cm and CD=12cm.
Since, it is a trapezoid, then AB will be parallel to CD, thus
∠BAC=∠DCA (Alternate angles)
Also, it is given that ∠DAC=∠BAC
⇒∠DAC=∠DCA
Also, ∠ACD=∠ACB( Angle bisector)
Therefore, If the angles are equal, then the corresponding sides will also be equal. Hence, △ABC and △ACD are isosceles triangle, therefore
AB=BC=9cm and CD=AD=12cm
Now, the perimeter of trapezoid is the sum of all the four sides of the trapezoid, therefore
Perimeter=AB+AD+CD+BC
Perimeter=9+9+12+12
Perimeter=42cm
The director would have to pay $40.47.
If each scholar eats one slice of pizza, then there would be two pizza pies because 8 slices plus another 8 slices in 16
8+8=16
If all of them eat another .5 slice, adding up the halves would equal 8
.5 x 16 = 8
In total, the director would have to buy three pizzas which equals up to our total of $40.47
Answer:
![A=4.86\sqrt{3}\ m^2](https://tex.z-dn.net/?f=A%3D4.86%5Csqrt%7B3%7D%5C%20m%5E2)
Step-by-step explanation:
The complete question in the attached figure
we know that
The area of triangle is given by the formula
![A=\frac{1}{2}(b)(h)](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%28b%29%28h%29)
we have
----> given problem
Find the value of b
In the right triangle of the figure (a sail)
---> by TOA (opposite side divided by the adjacent side)
we have
![tan(60^o)=\sqrt{3}](https://tex.z-dn.net/?f=tan%2860%5Eo%29%3D%5Csqrt%7B3%7D)
![h=5.4\ m](https://tex.z-dn.net/?f=h%3D5.4%5C%20m)
substitute
![\sqrt{3}=\frac{5.4}{b}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D%3D%5Cfrac%7B5.4%7D%7Bb%7D)
solve for b
![b=\frac{5.4}{\sqrt{3}}=1.8\sqrt{3}\ m](https://tex.z-dn.net/?f=b%3D%5Cfrac%7B5.4%7D%7B%5Csqrt%7B3%7D%7D%3D1.8%5Csqrt%7B3%7D%5C%20m)
<em>Find the area</em>
![A=\frac{1}{2}(1.8\sqrt{3})(5.4)](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%281.8%5Csqrt%7B3%7D%29%285.4%29)
![A=4.86\sqrt{3}\ m^2](https://tex.z-dn.net/?f=A%3D4.86%5Csqrt%7B3%7D%5C%20m%5E2)
Answer:
2 out of 5 chance of being red
Step-by-step explanation:
Right now his test scores average to 78.5 which mean if he wants to get an 80 for the final average, the lowest he can score is 94%