Question

Find the value of x

A. 20
B. 28
C. 10
D. 50/7

Answer 1

Answer:

x=28

Step-by-step explanation:

Step 1, comparing triangles:

Let us look at $\triangle ABC$ and $\triangle ADE$.

• They both share $\angle A$ ($\angle A=\angle A$)

• $\angle ABC = \angle BDE$ (Corresponding Angle Theorem)
• $\angle ACB = \angle CED$ (Corresponding Angle Theorem)

Therefore, because of AAA (Angle Angle Angle), $\triangle ABC$ and $\triangle ADE$ are similar.

Step 2:

Because the two triangles are similar, their sides should be proportional. Notice that $\overline{AB}$ and $\overline {AD}$ should be proportional.

Therefore, $\overline{AB}$: $\overline {AD}$ =

$12:30+12=\\12:42=\\2:7$

(Note, $\overline {AD}$ =  $\overline{AB}$+ $\overline{BD}$=12+30)

Step 3:

We figured out that  $\triangle ABC$  and  $\triangle ADE$ have proportional sides of 2:7. Therefore,  $\overline{BC}$ and $\overline{DE}$ should also have a ratio of 2:7.

$8: \overline{DE}=2:7\\8:\overline{DE}=8:28\\\overline{DE}=\fbox{28}$

x=28

I hope this helps! Let me know if you have any questions :)

Answer 2

Answer:

x = 20

Step-by-step explanation:

If we look at the given diagram, we will see that ΔABC and ΔADE are similar. Because they a similar we know that corresponding sides are in proportion. In order to solve this question, we need to know what the coefficient of similarity is.

AB and AD are corresponding sides, in order to get from 12 to 30 we need to multiple 12 by 2.5. That means that the coefficient of similarity between the two triangles is 2.5. To get x (length of DE) we need to multiply the length of BC by the coefficient of similarity. And so we get...

x = 2.5(BC)

x = 2.5(8)

x = 20