Answer:
6 cm²
Step-by-step explanation:
Since 3 side lengths are given, I assume that this figure is a triangle. The area of a triangle can be determined by using hero's formula.
![\text{Area of triangle} = \sqrt{\text{s(s - a)(s - b)(s - c)}](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20triangle%7D%20%3D%20%5Csqrt%7B%5Ctext%7Bs%28s%20-%20a%29%28s%20-%20b%29%28s%20-%20c%29%7D)
⇒ s = Perimeter/2
⇒ a, b, and c = side lenths of triangle
<u>Replacing a, b, and c as the given side lengths:</u>
![\implies \text{Area of triangle} = \sqrt{\text{s(s - 5)(s - 3)(s - 4)}](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctext%7BArea%20of%20triangle%7D%20%3D%20%5Csqrt%7B%5Ctext%7Bs%28s%20-%205%29%28s%20-%203%29%28s%20-%204%29%7D)
<u>Determining the perimeter of the triangle:</u>
![\text{Perimeter of triangle = Sum of it's side lengths}](https://tex.z-dn.net/?f=%5Ctext%7BPerimeter%20of%20triangle%20%3D%20Sum%20of%20it%27s%20side%20lengths%7D)
![\implies \text{Perimeter of triangle =}\ 5 + 4 + 3](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctext%7BPerimeter%20of%20triangle%20%3D%7D%5C%205%20%2B%204%20%2B%203)
![\implies \text{Perimeter of triangle =}\ 12 \ \text{cm}](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctext%7BPerimeter%20of%20triangle%20%3D%7D%5C%2012%20%5C%20%5Ctext%7Bcm%7D)
<u>Determining the half of perimeter:</u>
![\text{Half of perimeter} = s = \dfrac{\text{Perimeter}}{2}](https://tex.z-dn.net/?f=%5Ctext%7BHalf%20of%20perimeter%7D%20%3D%20s%20%3D%20%5Cdfrac%7B%5Ctext%7BPerimeter%7D%7D%7B2%7D)
![\implies s = \dfrac{12}{2}](https://tex.z-dn.net/?f=%5Cimplies%20s%20%3D%20%5Cdfrac%7B12%7D%7B2%7D)
![\implies s = 6](https://tex.z-dn.net/?f=%5Cimplies%20s%20%3D%206)
<u>Replacing the value of "s" in the formula:</u>
![\implies \text{Area of triangle} = \sqrt{\text{6(6 - 5)(6 - 3)(6 - 4)}](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctext%7BArea%20of%20triangle%7D%20%3D%20%5Csqrt%7B%5Ctext%7B6%286%20-%205%29%286%20-%203%29%286%20-%204%29%7D)
<u>Evaluating the area:</u>
![\implies \text{Area of triangle} = \sqrt{\text{6(6 - 5)(6 - 3)(6 - 4)}](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctext%7BArea%20of%20triangle%7D%20%3D%20%5Csqrt%7B%5Ctext%7B6%286%20-%205%29%286%20-%203%29%286%20-%204%29%7D)
![\implies \text{Area of triangle} = \sqrt{\text{6(1)(3)(2)}](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctext%7BArea%20of%20triangle%7D%20%3D%20%5Csqrt%7B%5Ctext%7B6%281%29%283%29%282%29%7D)
![\implies \text{Area of triangle} = \sqrt{\text{6(6)}](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctext%7BArea%20of%20triangle%7D%20%3D%20%5Csqrt%7B%5Ctext%7B6%286%29%7D)
![\implies \text{Area of triangle} = 6 \ \text{cm}^{2}](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctext%7BArea%20of%20triangle%7D%20%3D%206%20%5C%20%5Ctext%7Bcm%7D%5E%7B2%7D)
Answer:
15 hrs.
Step-by-step explanation:
204/4 = 51 miles per hrour
765/51 = 15 hrs.
Answer:
4 questions
Step-by-step explanation:
90% is the same as multiplying a number by 0.9. Let's say the number of questions on the quiz is x. This means the amount she got right was 0.9x. We are given this is 36, so we can set them equal and simplify:
0.9x = 36
x = 40
She must have gotten 40 - 36, or 4 questions wrong.
Answer:
the distance is 3/4
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask me in the comments below :)
When you can divide, or multiply by the same number. for numerator and denominator.