D and E are points on the sides AB and AC respectively of a $\triangle\text{ABC}$ such that DE || BC:
If AD = 3.6cm, AB = 10cm and AE = 4.5cm, find EC and AC.
If AD = 3.6cm, AB = 10cm and AE = 4.5cm, find EC and AC.
Download our app for free and get started
In $\triangle\text{ABC},$ it is given that DE || BC.
Applying Thales' theorem, we get:
$\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}$
$\therefore\text{AD}=3.6,\text{AB}=10\text{cm},\text{AE}=4.5\text{cm}$
$\therefore\text{DB}=10-3.6=6.4\text{cm}$
or, $\frac{3.6}{6.4}=\frac{4.5}{\text{EC}}$
or, $\text{EC}=\frac{6.4\times4.5}{3.6}$
or, $\text{EC}=8\text{cm}$
Thus, $\text{AC}=\text{AE}+\text{EC}$
$=4.5 +8=12.5\text{cm}$
Applying Thales' theorem, we get:
$\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}$
$\therefore\text{AD}=3.6,\text{AB}=10\text{cm},\text{AE}=4.5\text{cm}$
$\therefore\text{DB}=10-3.6=6.4\text{cm}$
or, $\frac{3.6}{6.4}=\frac{4.5}{\text{EC}}$
or, $\text{EC}=\frac{6.4\times4.5}{3.6}$
or, $\text{EC}=8\text{cm}$
Thus, $\text{AC}=\text{AE}+\text{EC}$
$=4.5 +8=12.5\text{cm}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1View SolutionProve that the ratio of the perimeters of two similar triangles is the same as the ratio of their corresponding sides.
- 2In a $\triangle\text{ABC},\text{AD}$ is the bisector of $\angle\text{A}.$View Solution
If AB = 5.6cm, AC = 4cm and DC = 3cm, find BC.
- 3View SolutionABCD is a quadrilateral in which AD = BC. If P, Q, R, S be the midpoints of AB, AC, CD and BD respectively, show that PQRS is a rhombus.
- 4In the given figure, $\triangle\text{ODC}\sim\triangle\text{OBA},\angle\text{BOC}=115^\circ$ and $\angle\text{CDO}=70^\circ.$View Solution
Find- $\angle\text{DOC}$
- $\angle\text{DCO}$
- $\angle\text{OAB}$
- $\angle\text{OBA}$
- 5In a $\triangle\text{ABC},\text{AD}$ is the bisector of $\angle\text{A}.$ If AB = 5.6cm, BD = 3.2cm and BC = 6cm, find AC.View Solution
- 6Two triangles DEF and GHK are such that $\angle\text{D}=48^\circ$ and $\angle\text{H}=57^\circ.$ If $\triangle\text{DEF}\sim\triangle\text{GHK}$ then find the measure of $\angle\text{F}.$View Solution
- 7View SolutionThe sides of certain triangles are given below. Determine them are right triangles:
9cm, 16cm, 18cm. - 8A man goes $10\ m$ due south and then $24\ m$ due west. How far is he from the starting point?View Solution
- 9View SolutionFind the lenght of each side of a rhombus whose diagonals are 24cm and 10cm. long.
- 10View SolutionFind the height of an equilateral triangle of side 12cm.