240 = 2 × 120
120 = 2 × 60
60 = 2 × 30
30 = 2 × 15
15 = 3 × 5
The 2, 2, 2, 2, 3 and 5 are all the prime factors of 240. So, 2^4 × 3 × 5
1500 = 3 × 500
500 = 5 × 100
100 = 5 × 20
20= 5 × 4
4 = 2 × 2
The 3, 5, 5, 5, 2 and 2 are all the prime factors of 1500. So, 2² + 3 + 5³
Answer:
29.4
Step-by-step explanation:
So the ratio of boys to girls is 12:24.. now, is that an equivalent ratio as 2 boys for 4 girls? or 2:4? let's see.
![\bf \cfrac{boys}{girls}\qquad 12:24\qquad \cfrac{12}{24}\implies \boxed{\cfrac{1}{2}} \\\\\\ \cfrac{boys}{girls}\qquad 2:4\qquad \cfrac{2}{4}\implies \boxed{\cfrac{1}{2}}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7Bboys%7D%7Bgirls%7D%5Cqquad%2012%3A24%5Cqquad%20%5Ccfrac%7B12%7D%7B24%7D%5Cimplies%20%5Cboxed%7B%5Ccfrac%7B1%7D%7B2%7D%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7Bboys%7D%7Bgirls%7D%5Cqquad%202%3A4%5Cqquad%20%5Ccfrac%7B2%7D%7B4%7D%5Cimplies%20%5Cboxed%7B%5Ccfrac%7B1%7D%7B2%7D%7D)
you could start simplifying the 12/24 fraction by dividing by some common multiple, say 2, and get 6/12, then divide by 3 and get 2/4 and stop there.
then you'll notice that 12/24 is really 2/4 in disguise.
Answer:
![\large\boxed{A_\triangle=25\sqrt{15}\ cm^2}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7BA_%5Ctriangle%3D25%5Csqrt%7B15%7D%5C%20cm%5E2%7D)
Step-by-step explanation:
Look at the picture.
The formula of an area of a triangle:
![A_\triangle=\dfrac{bh}{2}](https://tex.z-dn.net/?f=A_%5Ctriangle%3D%5Cdfrac%7Bbh%7D%7B2%7D)
<em>b</em><em> - base</em>
<em>h</em><em> - height</em>
<em />
We need a length of a height.
Use the Pythagorean theorem:
![leg^2+leg^2=hypotenuse^2](https://tex.z-dn.net/?f=leg%5E2%2Bleg%5E2%3Dhypotenuse%5E2)
We have:
![leg=5,\ leg=h,\ hypotenuse=20](https://tex.z-dn.net/?f=leg%3D5%2C%5C%20leg%3Dh%2C%5C%20hypotenuse%3D20)
Substitute:
![5^2+h^2=20^2](https://tex.z-dn.net/?f=5%5E2%2Bh%5E2%3D20%5E2)
<em>subtract 25 from both sides</em>
![h^2=375\to h=\sqrt{375}\\\\h=\sqrt{(25)(15)}\\\\h=\sqrt{25}\cdot\sqrt{15}\\\\h=5\sqrt{15}\ cm](https://tex.z-dn.net/?f=h%5E2%3D375%5Cto%20h%3D%5Csqrt%7B375%7D%5C%5C%5C%5Ch%3D%5Csqrt%7B%2825%29%2815%29%7D%5C%5C%5C%5Ch%3D%5Csqrt%7B25%7D%5Ccdot%5Csqrt%7B15%7D%5C%5C%5C%5Ch%3D5%5Csqrt%7B15%7D%5C%20cm)
Calculate the area:
![A_\triangle=\dfrac{(10)(5\sqrt{15})}{2}=\dfrac{50\sqrt{15}}{2}=25\sqrt{15}\ cm^2](https://tex.z-dn.net/?f=A_%5Ctriangle%3D%5Cdfrac%7B%2810%29%285%5Csqrt%7B15%7D%29%7D%7B2%7D%3D%5Cdfrac%7B50%5Csqrt%7B15%7D%7D%7B2%7D%3D25%5Csqrt%7B15%7D%5C%20cm%5E2)