Question

Quadrilateral ABCD is similar to quadrilateral EFGH. What is the length of
segment BC?

Answer 1

So Basically, these are similar. So that means that (2x/5.5)=(3x-3/7.5). Then when you cross multiply, you find that x=11. So that means BA/FE=22/5.5=4. You can verify by checking (3*11-3)/7.4=4. So now that you know the scale factor is 4, just do 4*8=32.

Answer 2

Answer: The required length of BC is 32 units.

Step-by-step explanation: Given that the quadrilaterals ABCD and EFGH are similar to each other.

We are to find the length of side BC.

From the figure, we note that

AB = 2x, CD = 3x - 3, EF = 5.5, FG = 8, GH = 7.5 and EH = 7.

Since the corresponding sides of similar figures are proportional, so we get

`(AB)/(EF)=(CD)/(GH)\\\\\\\Rightarrow (2x)/(5.5)=(3x-3)/(7.5)\\\\\\\Rightarrow (2x)/(55)=(3x-3)/(75)\\\\\Rightarrow 150x=165x-165\\\\\Rightarrow 165x-150x=165\\\\\Rightarrow 15x=165\\\\\Rightarrow x=(165)/(15)\\\\\Rightarrow x=11.`

Also, we can write

`(BC)/(FG)=(CD)/(GH)\\\\\\\Rightarrow (BC)/(8)=(3*11-3)/(7.5)\\\\\\\Rightarrow (BC)/(80)=(30)/(75)\\\\\\\Rightarrow BC=(30)/(75)*80\\\\\\\Rightarrow BC=(2)/(5)*80\\\\\Rightarrow BC=32.`

Thus, the required length of BC is 32 units.