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

$\dfrac{AB}{EF}=\dfrac{CD}{GH}\\\\\\\Rightarrow \dfrac{2x}{5.5}=\dfrac{3x-3}{7.5}\\\\\\\Rightarrow \dfrac{2x}{55}=\dfrac{3x-3}{75}\\\\\Rightarrow 150x=165x-165\\\\\Rightarrow 165x-150x=165\\\\\Rightarrow 15x=165\\\\\Rightarrow x=\dfrac{165}{15}\\\\\Rightarrow x=11.$

Also, we can write

$\dfrac{BC}{FG}=\dfrac{CD}{GH}\\\\\\\Rightarrow \dfrac{BC}{8}=\dfrac{3\times11-3}{7.5}\\\\\\\Rightarrow \dfrac{BC}{80}=\dfrac{30}{75}\\\\\\\Rightarrow BC=\dfrac{30}{75}\times80\\\\\\\Rightarrow BC=\dfrac{2}{5}\times80\\\\\Rightarrow BC=32.$

Thus, the required length of BC is 32 units.