Question

Given that ∠ABD is similar to ∠ACE, what is the value of x? Round your answer to the nearest tenth.

Answer 1

I believe the correct image of the triangle is the one I attach (see attached pic).

Since we know that:

m ∠ABD = m ∠ACE

where m stands for measure of the angle

 

Then we can also say that:

m ∠ADB = m ∠ AEC

 

By virtue of two similar angles of two triangles, therefore we can say that Δ ABD and Δ ACE are congruent triangles. Hence the ratios of the sides of the triangles are equal, that is:

AB / BC = AD / DE = CE / BD

where AD = x, hence:

AB / BC = x / DE = CE / BD

 

Calculating for x using the the right equality:

x / DE = BD / CE

x / 2.7 = 7.4 / 5

x = 3.99 cm = 4 cm