Question

Please help me work this out and explain it.

Answer 1

So triangle ABC and triangle CDE are the same triangle. The triangle ABC is just a simplified version of triangle CDE. So, for the length of C,E it is 24in. The length of the equivalent side of C,E is A,C which equals 8cm. So we will do the length of side C,E divided by the length of side A,C. (24 divided by 8)= 3. Since the anwser is 3 we now know that side A,C multiplied by 3 equals side C,E. So now you just do Side B,C multiplied by 3 to get the D,E side. (5 x 3) = 15. So side D,E equals 15in. To find Side B,A you will need to do the same as you did for side C,E earlier. So take side D,C and divide it by 3 (18 divided by 3 = 6) Side D,E now equals 6in.

Answer 2

a) DE = 15 cm

b) AB = 6 cm

Explanation:

Explanation #a)

- Relating the triangle ABC with triangle DCE, a scale factor fomula is used;

`{ \rm{ \frac{ \bar{DE}}{ \bar{BC} }} = \frac{ \bar{CE}}{ \bar{AC} } } \\ \\ { \rm{ \frac{\bar{DE}}{5} = (24)/(8) }} \\ \\ { \rm{\bar{DE}} = (24 * 5)/(8) } \\ \\ { \rm{\bar{DE}} = 15 \: cm}`

Explanation #b)

`{ \rm{ \frac{ \bar{CE}}{ \bar{AC}} } = \frac{ \bar{CD}}{ \bar{AB} }} \\ \\ { \rm{ (24)/(8) = \frac{18}{\bar{AB}} }} \\ \\ { \rm{\bar{AB} = (18 * 8)/(24) }} \\ \\ { \rm{\bar{AB} = 6 \: cm}}`

- Therefore, the scale factor is 2, triangle CDE = 2ABC

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