# Video: Pack 5 β’ Paper 1 β’ Question 11

Pack 5 β’ Paper 1 β’ Question 11

02:57

### Video Transcript

Triangles π΄π΅πΆ and π΄π·πΈ are mathematically similar. π΄πΆ is equal to five, π΄π΅ is equal to π¦, π΅π· is equal to six, π·πΈ is equal to 12, πΆπΈ is equal to π₯, and π΅πΆ is equal to eight. Work out the values of π₯ and π¦.

As the two triangles are similar, their corresponding lengths will have the same scale factor. For the purposes of this question, weβll call the scale factor π. If we firstly considered the corresponding length π΅πΆ and π·πΈ, then eight multiplied by π the scale factor is equal to 12. Dividing both sides of this equation by eight gives us π is equal to 12 over eight. Simplifying this fraction by dividing the top and bottom by four gives us π is equal to three over two. This means that the scale factor is three over two or 1.5.

In order to calculate the value of π₯, we need to consider the corresponding lengths π΄πΆ and π΄πΈ. Five multiplied by three over two is equal to π₯ plus five. This is because the length of π΄πΆ is five and the length of π΄πΈ is π₯ plus five. Multiplying the left-hand side gives us 15 over two. Multiplying both sides of this equation by two gives us 15 is equal to two π₯ plus 10. Subtracting 10 from both sides of this equation gives us two π₯ is equal to five. Dividing both sides by two gives us a value of π₯ of five over two or 2.5.

In order to work out the value of π¦, we need to consider the corresponding lengths π΄π΅ and π΄π·. The length of π΄π΅ is π¦ and the length of π΄π· is π¦ plus six. Therefore, π¦ multiplied by our scale factor three over two is equal to π¦ plus six. Simplifying the left-hand side gives us three π¦ over two. Multiplying both sides of this equation by two gives us three π¦ is equal to two π¦ plus 12. And finally, subtracting two π¦ from both sides of this equation gives us a value for π¦ equal to six.

If the two triangles π΄π΅πΆ and π΄π·πΈ are mathematically similar, then π₯ equals five over two and π¦ equals six.