Answer: B) Corresponding sides of the two triangles have the ratio of 4:1, which proves SSS similarity. The length of the lake is 132m.
Step-by-step explanation: <u>Similar</u> <u>Triangles</u> are triangles with corresponding sides proportional to each other.
One way to determine if two triangles are similar is a theorem called Side-Side-Side Similarity Theorem or <u>SSS</u> <u>similarity</u> and it states that two triangles are similar if corresponding angles are equal and corresponding sides are proportional.
The triangles below are similar and they obey this theorem because we observe that the angles are the same and the corresponding sides are proportional:
![\frac{big}{small}=\frac{212}{53}=\frac{60}{15}=4](https://tex.z-dn.net/?f=%5Cfrac%7Bbig%7D%7Bsmall%7D%3D%5Cfrac%7B212%7D%7B53%7D%3D%5Cfrac%7B60%7D%7B15%7D%3D4)
So, the ratio of bigger triangle and smaller triangle is 4:1.
With that ratio and suppose length is represented as L:
![\frac{L}{33} =4](https://tex.z-dn.net/?f=%5Cfrac%7BL%7D%7B33%7D%20%3D4)
L = 132
The length of the lake is 132m.
Thus, the answer for this question is
1) The similarity of the triangles is proved by SSS similarty;
2) Ratio of proportion is 4:1;
3) Length of the lake is 132m;
I found same type of question on Brainly!
If you want you can check from other people who wrote the answer!
There are 6 2/3 cup servings in a 4 cup container.
Answer:
![Width = 5x + 1](https://tex.z-dn.net/?f=Width%20%3D%205x%20%2B%201)
Step-by-step explanation:
Given
![Area = 10x^2 + 5x](https://tex.z-dn.net/?f=Area%20%3D%2010x%5E2%20%2B%205x)
![Length = 5x](https://tex.z-dn.net/?f=Length%20%3D%205x)
Required (Missing)
Determine the Width?
Area is calculated as:
![Area = Length * Width](https://tex.z-dn.net/?f=Area%20%3D%20Length%20%2A%20Width)
Substitute values for Area and Length
![10x^2 + 5x = 5x * Width](https://tex.z-dn.net/?f=10x%5E2%20%2B%205x%20%3D%205x%20%2A%20Width)
Factorize the right hand side
![5x(5x + 1) = 5x * Width](https://tex.z-dn.net/?f=5x%285x%20%2B%201%29%20%3D%205x%20%2A%20Width)
Divide both sides by 5x
![5x + 1 = Width](https://tex.z-dn.net/?f=5x%20%2B%201%20%3D%20Width)
<em>Hence, the width of the model is 5x + 1</em>
The answer is: "
40 % " .
_______________________________________________Note:_______________________________________________ If "3/5" of the students ride the bus, then "2/5" do not ride the bus".
Since: "3/5" + "2/5" = "(3 + 2)" / 5 = 5/5 = "1" (as in "1 whole").
1 – (3/5) = (5/5) – (3/5) = (5 – 3) / 5 = 2/5.
________________________________________________Now, express: "2/5" as a percentage ;
→ "2/5" = "x / 100 " ; Solve for "x"
Cross-multiply: Note:
→ Given: "
![\frac{a}{b}](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba%7D%7Bb%7D)
" = "
![\frac{c}{d}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bc%7D%7Bd%7D)
" ;
→ " bc = ad" ; {" b
![\neq](https://tex.z-dn.net/?f=%20%5Cneq%20)
0 ; d
![\neq](https://tex.z-dn.net/?f=%20%5Cneq%20)
0 "} .
_______________________________________________________As such:
→ "
![\frac{2}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7B5%7D)
" = "
![\frac{x}{100}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7B100%7D)
" ;
→ " 5x = (2)*(100) " ;
→ Solve for "x" ;
→ " 5x = 200 " ;
→ Divide each side of the equation by "5" ;
to isolate "x" on one side of the equation; & to solve for "x" ;
→ " 5x / 5
= 200 / 5 " ;
to get:
→ "
x = 40 " ;
_________________________________________So; we have:
→ "2/5" = "
40 / 100 " ;
→ "2/5" = "
40 % " .
____________________________________________The answer is: "
40 % " .
____________________________________________