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:
So, the ratio of bigger triangle and smaller triangle is 4:1.
With that ratio and suppose length is represented as L:
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;
He travels approximately 45 miles
Applying the same-side interior angles theorem, the value of x is: D. 20.
<h3>What is the Same-Side Interior Angles Theorem?</h3>
The same-side interior angles are said to be supplementary to each other if they lie on two parallel lines, according to the same-side interior angles theorem.
Given that lines a and b are parallel, the two angles shown in the image given are same-side interior angles, therefore:
6x + 3x = 180 [according to the same-side interior angles theorem]
Combine like terms
9x = 180
Divide both sides by 9
9x/9 = 180/9 [division property of equality]
x = 20
The value of x is therefore: D. 20.
Learn more about the same-side interior angles theorem on:
brainly.com/question/16976757
#SPJ1
65% of 1 = .65
65/100 = 13/20
65/100 = .65
65/100 = .65¢
It looks like the first thing you have to find is their GCF, ya reckon ?
The factors of 56 are 1, 2, 4, 7, 8, 13, 28, and 56 .
The factors of 64 are 1, 2, 4, 8, 16, 32, and 64 .
The common factors are 1, 2, 4, and 8 .
The greatest one is 8 .
56/8 = 7
64/8 = 8
56 plus 64 = (8 times 7) plus (8 times 8)
<span>56 plus 64 = </span><u>8 times (7 plus 8)</u><span> <== that's the answer</span>
Check it out:
<span>56 plus 64 = </span><u>120</u>
<span>8 times (7 plus 8) = 8 times 15 = </span><u>120</u><span> </span>