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antiseptic1488 [7]
3 years ago
10

Triangle DEF is similar to triangle ABC, and the length of EF is 5cm. What are the lengths of sides DE is 6cm and DF is 8cm cent

imeters?
Mathematics
1 answer:
ra1l [238]3 years ago
6 0

Answer:

Step-by-step explanation:

Given that,

∆DEF is similar to ∆ABC

∆DEF ≈ ∆ABC

Then, using similar triangle properties

DE / AB = DF /AC = EF / BC

Given that,

EF = 5cm, DE = 6cm and DF = 8cm

6 / AB = 8 / AC = 5 / BC

We need one more data, to solve this problem, so the question is not complete, but let assume AC is 16cm

Then, we can find AB and BC

So, taking each part of the equation

6 / AB = 8 / AC

Since we assumed AC = 16cm

6 / AB = 8 / 16 = ½

6×2 = AB

AB = 12cm

Taking the other parts of the equation

8 / AC = 6 / BC

8 / 16 = 5 / BC

½ = 5 / BC

Bc = 2 × 5

BC = 10cm.

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Answer:

The correct answer is 25

Step-by-step explanation:

See the attached figure.

SAS similarity theorem mean that when two triangles have corresponding angles are congruent and corresponding sides with identical ratios the triangles are similar.

So, if ΔONM similar ΔSRQ by the SAS similarity theorem

∴∠N = ∠R

And

\frac{NM}{RQ} =\frac{NO}{RS}

given that NM = 10 , NO = 8 , QR = x , RS = 20

∴\frac{10}{x} =\frac{8}{20}

∴x=\frac{10*20}{8} =25

So, the value of x will make ONM similar SRQ by the SAS similarity theorem = 25

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The following are the ages of 13 history teachers in a school district. 24, 27, 29, 29, 35, 39, 43, 45, 46, 49, 51, 51, 56 Notic
pishuonlain [190]

The five-number summary and the interquartile range for the data set are given as follows:

  • Minimum: 24.
  • Lower quartile: 29.
  • Median: 43.
  • Upper quartile: 50.
  • Maximum: 56.
  • Interquartile range: 50 - 29 = 21.

<h3>What are the median and the quartiles of a data-set?</h3>

  • The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.
  • The first quartile is the median of the first half of the data-set.
  • The third quartile is the median of the second half of the data-set.
  • The interquartile range is the difference between the third quartile and the first quartile.

In this problem, we have that:

  • The minimum value is the smallest value, of 24.
  • The maximum value is the smallest value, of 56.
  • Since the data-set has odd cardinality, the median is the middle element, that is, the 7th element, as (13 + 1)/2 = 7, hence the median is of 43.
  • The first quartile is the median of the six elements of the first half, that is, the mean of the third and fourth elements, mean of 29 and 29, hence 29.
  • The third quartile is the median of the six elements of the second half, that is, the mean of the third and fourth elements of the second half, mean of 49 and 51, hence 50.
  • The interquartile range is of 50 - 29 = 21.

More can be learned about five number summaries at brainly.com/question/17110151

#SPJ1

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