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;
6,300-530 and that gives you the answer
The least common multiple is 2
The slope is already given in the question, so we only ned to solve for the y-intercept using y = mx + b.
4 = 3(1) + b
4 = 3 + b
4 - 3 = 3 + b - 3
1 = b
Now, write the equation in slope-intercept form.
y = 3x + 1
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Best of Luck,
Wolfyy :)
Let us assume the two numbers to be "x" and "y".
Then
xy = - 24
x = - (24/y)
And
x + y = 2
Putting the value of x from the first equation in the second equation, we get
x + y = 2
- (24/y) + y = 2
- 24 + y^2 = 2y
y^2 - 2y - 24 = 0
y^2 - 6y + 4y - 24 = 0
y(y - 6) + 4(y - 6) = 0
(y - 6) (y + 4) = 0
When
y - 6 = 0
y = 6
Then
x + y = 2
x + 6 = 2
x = 2 - 6
= -4
And when
y + 4 = 0
y = -4
Then
x + y = 2
x - 4 = 2
x = 2 + 4
= 6
So the two unknown numbers are -4 and 6.