Question

A scientist looking at a sample of infected tissue through a microscope wants to find the length x, in microns, across a damaged blood cell, as represented in the sketch above. The lengths represented by AB, EB, BD, and CD were determined to be 26 microns, 22 microns, 11 microns, and 12 microns, respectively. Given that the measure of $\angle AEB$ is equal to the measure of $\angle CDB$, what is the value of x?

Answer 1

In $△ABE$ and $△CBD$,

$\angle AEB=\angle CDB$ ....Given

$\angle ABE=\angle CBD$ ...Vertically opposite angles

$\therefore △ABE\sim △CBD$ ...A.A. test of similarity

$\therefore \frac{AB}{BC}=\frac{BE}{BD}=\frac{AE}{CD}$ ...C.S.S.T

$\frac{22}{11}=\frac{x}{12}$

$x=24$ microns