Question

If AD = 2.5 cm, BD = 3.0 cm and AE = 3.75 cm, find the length of AC.

Answer 1

Hint: Consider a triangle ABC and points D and E in between AB and AC respectively such that DE is parallel to BC. Apply proportionality theorem in the line segments AE, CE, AD and BD. Get CE and then find AC.

Complete step-by-step answer:
Consider the above figure.
We are given that AD = 2.5 cm, BD = 3.0 cm, AE = 3.75 cm.
We need to find AC.
It can be easily observed that AC= AE + CE.
To get AC we must know CE.
In order to find CE, we shall use proportionality theorem.
The proportionality theorem states that-
A line segment drawn parallel to any side of the triangle such that it
join the two distinct points on its two sides then the line segment divides the two sides in the same ratio.
So following this theorem it can be concluded that-
$\dfrac{{AE}}{{CE}} = \dfrac{{AD}}{{BD}}$
Where DE is the line segment drawn parallel to the side BC.
$
  \dfrac{{3.75}}{{CE}} = \dfrac{{2.5}}{{3.0}} \\
  CE = \dfrac{{3.75 \times 3.0}}{{2.5}} \\
  CE = 4.50 \\
$
AC = AE + CE
AC = 3.75 + 4.50
AC = 8.25 cm
So, the length of AC is 8.25 cm.

Note: Since no diagram was given with the question, it was important to collect the information from the question and make the figure as simple as possible. Here this problem could have been solved by the use of congruence of triangles.