Question

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

(Side AD is x, side DE is 2.7 cm, side CE is 7.4 cm, side CB is y, side AB is 6.8 cm, and side BD((cutting across the middle)) is 5.0 cm).

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