Question

Suppose that in a triangle ABC, DE || BC, and if DB = 5.4 cm, AD = 1.8 cm, EC = 7.2 cm, then find AE.

Answer 1

Hint: To solve this problem we need to first know the Basic Proportionality Theorem or BPT theorem.
According to basic proportionality theorem, If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. To solve the given question, we will first draw the figure according to the given details and then use the BPT theorem to find the value of AE.

Complete step-by-step answer:
We are given a $\Delta ABC$ in which DE || BC, and if DB = 5.4 cm, AD = 1.8 cm, EC = 7.2 cm and we have to find AE.
First we will draw the figure of the triangle according to the data given to us,

Now there is rule for the triangles known as Basic proportionality theorem according to which if a line drawn parallel to a side of triangle then it divides other two sides in same ratio,
Applying this theorem in our triangle we get,
$\dfrac{AD}{DB}=\dfrac{AE}{EC}$
Now putting the values DB = 5.4 cm, AD = 1.8 cm, EC = 7.2 cm, we get
$\dfrac{1.8}{5.4}=\dfrac{AE}{7.2}$
Cross multiplying we get,
$AE=\dfrac{1.8\times 7.2}{5.4}=2.4$
Hence we get the length of the AE in the $\Delta ABC$ as 2.4 cm

Note: You need to know the Basic proportionality theorem of triangles in order to solve this triangle and also remember it for future problems also. You can also solve this question by taking the ratio, $\dfrac{AD}{AB}=\dfrac{AE}{AC}$ this is also valid but then you will have to write AB = AD + DB and AC = AE + EC. Then putting the required values and solving you will get the same answer.