The triangles below are similar. The ratio of the lengths of corresponding sides is 49 . a. What is the ratio (smaller to larger
) of the perimeters? b. What is the ratio (smaller to larger) of the areas? The image is of two similar triangles with proportionate side of each marked as 4 in. and 9 in. respectively.
1 answer:
Answer:
a.) 4 : 9
b.) 16 : 81
Explanation:
a.) Ratio of perimeter will still be
4 : 9
b.) The two similar triangles ΔABC and ΔDEF as shown from the attached figures. That is
AB/DE = AC/DF = BC/EF
It is apparent that ΔAPB and ΔDEQ are also similar as all respective angles are equal. Hence,
AB/DE = AP/DQ = BP/EQ
Moreso ΔABC = 1/2 × BC × AP and ΔDEF = 1/2 × EF × DQ and
ΔAPB/ΔDEQ = BC/EF × AP/DQ
But
AP/DQ = AB/DE = BC/EF
and hence
ΔAPB/ΔDEQ = BC/EF × BC/EF
= BC^2/EF^2 and as
BC/EF = AC/DF = AB/DE
ΔAPB/ΔDEQ = AC^2/DF^2 = BC^2/EF^2
= AB^2/DE^2
Hence if sides of two similar triangles are in the ratio a:b, their areas are in the proportion a^2:b^2
As in given case sides are in the ratio of 4:9.
ratio of their areas is 4^2:9^2 or 16:81.
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The answers to the given questions on the survey of students by the use of a Venn Diagram are;
A) Venn diagram attached
B) 57 Students
C) 811 Students
D) 785 Students
E) 67 Students
<h3>Understanding Venn Diagrams</h3>
We are given;
- Total number of Students = 1358
- Number of Students that plan to get a new job = 1194
- Number of Students that plan to attend graduate school = 306
- Number of Students that plan to buy a new car = 547
- Number of Students that plan to do all three things = 46
- Number of Students that plan to only attend graduate school = 28
- Number of Students that plan to get a job and buy a new car, but not attend graduate school = 432
- Number of Students that plan to get a new job and attend graduate school = 221
A) I have drawn a Venn Diagram to depict this given numbers of students and I have attached it.
B) From the venn diagram, we can see that the number of people that plan to attend graduate school and buy a new car, but not get a new job = 57
C) From the Venn diagram, we can calculate the number of students that do not plan to buy a new car is;
541 + 175 + 28 + 67 = 811
D) From the venn diagram, we can calculate the number of students plan to get a new job or buy a new car as;
541 + 175 + 12 + 57 = 785
E) From the venn diagram, we can see that the number of students that do not plan to get a new job, attend graduate school, nor buy a new car is; 67
The complete part of the question is;
A) Draw a Venn diagram that represents the situation consisting of 2. cardinalities.
B) How many people plan to attend graduate school and buy a new car, but not get a new job?
C) How many students do not plan a buy a new car?
D) How many students plan to get a new job or buy a new car?
E) How many students do not plan to get a new job, attend graduate school, nor buy a new car?
Read more about Venn Diagrams at; brainly.com/question/2099071
