Write and solve an equation of ratios based upon the fact that the small and large triangles shown are similar:
5 6
---- = ---------
14 6 + x
Then 30 + 5x = 84, and 5x = 54, and so x = 54/5, or 10.8, or 10 4/5.
Answer:
x = 7![\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D)
Triangle area formula: base * height * 1/2
We are given:
Base - 14 cm
Height - x
Using the pythagorean theroem (a^2 + b^2 = c^2) we can figure out the height.
We are given:
Side a - 14 / 2 = 7 cm
Side b - the height (x)
Side c - 14 (it's an equilateral triangle)
Now, substitute the given values:
7^2 + x^2 = 14^2
49 + x^2 = 196
x^2 = 147
x = ![\sqrt{147}](https://tex.z-dn.net/?f=%5Csqrt%7B147%7D)
x = 7![\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D)
If you do 138 divided by 12 you get 11.5, but since you can't have 11.5 full tables you know that there are only 11 full tables .
Answer:
![k=\frac{5}{4}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B5%7D%7B4%7D)
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
or
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
In this problem we have that
The line pass through the points
<em>Find the value of the constant of proportionality k</em>
For x=2/5, y=1/2
substitute
![k=\frac{y}{x}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7By%7D%7Bx%7D)
![k=\frac{1}{2}:\frac{2}{5}=\frac{5}{4}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B1%7D%7B2%7D%3A%5Cfrac%7B2%7D%7B5%7D%3D%5Cfrac%7B5%7D%7B4%7D)