Download Solve each proportion. 9. SOLUTION: Cross multiply. Solve for x. 10

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Solve each proportion.
9. SOLUTION: Cross multiply.
Solve for x.
10. SOLUTION: Cross multiply.
Solve for x.
11. SOLUTION: Cross multiply.
Solve for x.
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Solve for x.
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12. SOLUTION: Cross multiply.
Solve for x.
13. The ratio of the lengths of the three sides of a triangle is 5:8:10. If its perimeter is 276 inches, find the length of the
longest side of the triangle.
SOLUTION: Just as the ratio
or 5:8 is equivalent to
or 5x:8x , the extended ratio can be written as 5x:8x:10x. The perimeter is 276 inches, so the sum of the lengths of the sides is 276. Solve for x.
So the measures of the three sides are 5(12) or 60, 8(12) or 96, and 10(12) or 120. Thus the length of the longest side
is 120 inches.
14. CARPENTRY A board that is 12 feet long must be cut into two pieces that have lengths in a ratio of 3 to 2. Find
the lengths of the two pieces.
SOLUTION: Let x and 12 – x be the lengths of the two pieces. Form a proportion.
Solve for x.
So, the length of the other piece is (12 – 7.2) ft or 4.8 ft.
Thus the length of the two pieces are 7.2 ft and 4.8 ft.
Determine whether each pair of figures is similar. If so, write the similarity statement and scale factor. If
not, explain your reasoning.
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the length
the other piece is (12 – 7.2) ft or 4.8 ft.
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and of
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Thus the length of the two pieces are 7.2 ft and 4.8 ft.
Determine whether each pair of figures is similar. If so, write the similarity statement and scale factor. If
not, explain your reasoning.
15. SOLUTION: Step 1: Compare corresponding angles: All corresponding angles are congruent. Step 2: Compare corresponding sides:
Since
, the figures are not similar. No, the polygons are not similar because the corresponding sides are not proportional.
16. SOLUTION: Step 1: Compare corresponding angles: Since all of the angles in the polygons are right angles, they are all congruent to each other. Therefore,
corresponding angles are congruent. Step 2: Compare corresponding sides:
Since
, the corresponding sides of the polygons have the same scale factor, which is . Yes, the rectangles are similar because all of the corresponding angles are congruent and the corresponding sides
are proportional in a 3:2 ratio.
17. The two triangles in the figure below are similar. Find the value of x.
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Since
, the corresponding sides of the polygons have the same scale factor, which is . Yes,
the rectangles
are similar because all of the corresponding angles are congruent and the corresponding sides
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are proportional in a 3:2 ratio.
17. The two triangles in the figure below are similar. Find the value of x.
SOLUTION: If two triangles are similar, then their corresponding sides are proportional.
Form a proportion and solve for x. 18. PHOTOS IF the dimensions of a photo are 2 inches by 3 inches and the dimensions of a poster are 8 inches by 12
inches, are the photo and poster similar? Explan.
SOLUTION: Yes; the ratios are the same. Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning.
19. SOLUTION: By the Reflexive Property,
.
So,
by SAS Similarity.
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by SAS Similarity.
20. SOLUTION: .
So,
by SSS Similarity.
21. SOLUTION: No, the triangles are not similar because not all corresponding angles are congruent.
22. SOLUTION: Since
Yes,
, then congruent alternate interior angles are formed. Therefore,
. by the AA Similarity Post.
Find x.
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SOLUTION: Since
, then congruent alternate interior angles are formed. Therefore,
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Study
Yes,
by the AA Similarity Post.
. Find x.
24. SOLUTION: Solve for x.
25. SOLUTION: Solve for x.
26. STREETS Find the distance along Broadway between 37th St. and 36th St.
SOLUTION: Assuming that 38th street, 37th street and 36th street are parallel to each other, we can set up a proportion using the
triangle proportionality Theorem:
.
Solve for x.
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The distance between 37th St. and 36th St is 220 ft.
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Solve for x.
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26. STREETS Find the distance along Broadway between 37th St. and 36th St.
SOLUTION: Assuming that 38th street, 37th street and 36th street are parallel to each other, we can set up a proportion using the
triangle proportionality Theorem:
.
Solve for x.
The distance between 37th St. and 36th St is 220 ft.
Find the value of each variable.
27. SOLUTION: An angle bisector in a triangle separates the opposite side into two segments that are proportional to the lengths of
the other two sides.
28. SOLUTION: An angle bisector in a triangle separates the opposite side into two segments that are proportional to the lengths of
the other two sides.
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28. SOLUTION: An angle bisector in a triangle separates the opposite side into two segments that are proportional to the lengths of
the other two sides.
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