Question

4 figure efgh is a scaled copy of figure abcd. select all of the true statements. a. segment ef is twice as long as segment ab. b. the ratio of ab/bc is equivalent to the ratio of eh/hg. c. the scale factor from efgh to abcd is 2. d. the length of segment ad is 8 units. e. the area of efgh is twice the area of abcd. 5 a scale drawing of a rectangular park is 8 inches wide and 11 inches long. the actual park is 330 yards long. what is its area? a. 88 square yards b. 240 square yards c. 2,640 square yards d. 79,200 square yards

Explanation:

Step1: Analyze similar - figures property for question [4]

For two similar figures (where one is a scaled - copy of the other), the ratios of corresponding side - lengths are equal. Let the scale factor from \(ABCD\) to \(EFGH\) be \(k\).

Step2: Evaluate option A for question [4]

We don't have enough information to determine the relationship between \(EF\) and \(AB\) to say \(EF = 2AB\), so option A is not necessarily true.

Step3: Evaluate option B for question [4]

Since \(ABCD\) and \(EFGH\) are similar, \(\frac{AB}{BC}=\frac{EH}{HG}\) because the ratios of corresponding sides of similar figures are equal. So option B is true.

Step4: Evaluate option C for question [4]

If the scale factor from \(ABCD\) to \(EFGH\) is \(k\), the scale factor from \(EFGH\) to \(ABCD\) is \(\frac{1}{k}\). Without knowing the actual scale factor from \(ABCD\) to \(EFGH\), we can't say the scale factor from \(EFGH\) to \(ABCD\) is 2. So option C is not necessarily true.

Step5: Evaluate option D for question [4]

We have no information about the length of \(AD\), so option D is not necessarily true.

Step6: Evaluate option E for question [4]

If the scale factor between two similar figures is \(k\), the ratio of their areas is \(k^{2}\). If \(k = 2\), the area of \(EFGH\) is \(k^{2}=4\) times the area of \(ABCD\), not 2 times. So option E is not true.

Step7: Solve for the width of the actual park in question [5]

Let the scale factor be \(s\). We know that the length of the scale - drawing is 11 inches and the actual length is 330 yards. First, set up a proportion for the length: \(\frac{11\text{ inches}}{330\text{ yards}}=\frac{8\text{ inches}}{x\text{ yards}}\). Cross - multiply: \(11x=330\times8\), then \(x = \frac{330\times8}{11}=240\) yards.

Step8: Calculate the area of the actual park in question [5]

The area of a rectangle \(A = l\times w\), where \(l = 330\) yards and \(w = 240\) yards. So \(A=330\times240 = 79200\) square yards.

Answer:

[4] B. The ratio of \(\frac{AB}{BC}\) is equivalent to the ratio of \(\frac{EH}{HG}\).
[5] D. 79,200 square yards