Choose the correct answer from the given four options:
It is given that \( \triangle \mathrm{ABC} \sim \triangle \mathrm{DFE}, \angle \mathrm{A}=30^{\circ}, \angle \mathrm{C}=50^{\circ}, \mathrm{AB}=5 \mathrm{~cm}, \mathrm{AC}=8 \mathrm{~cm} \) and \( D F=7.5 \mathrm{~cm} \). Then, the following is true:
(A) \( \mathrm{DE}=12 \mathrm{~cm}, \angle \mathrm{F}=50^{\circ} \)
(B) \( \mathrm{DE}=12 \mathrm{~cm}, \angle \mathrm{F}=100^{\circ} \)
(C) \( \mathrm{EF}=12 \mathrm{~cm}, \angle \mathrm{D}=100^{\circ} \)
(D) \( \mathrm{EF}=12 \mathrm{~cm}, \angle \mathrm{D}=30^{\circ} \)
Given:
\( \triangle \mathrm{ABC} \sim \triangle \mathrm{DFE}, \angle \mathrm{A}=30^{\circ}, \angle \mathrm{C}=50^{\circ}, \mathrm{AB}=5 \mathrm{~cm}, \mathrm{AC}=8 \mathrm{~cm} \) and \( D F=7.5 \mathrm{~cm} \).
To do:
We have to choose the correct answer.
Solution:
From the figure,
$\angle B=\angle F$
$=180^{\circ}-(30^{\circ}+50^{\circ})$
$=100^{\circ}$
$A B=5 \mathrm{~cm}, A C=8 \mathrm{~cm}$ and $DF=7.5 \mathrm{~cm}$
Therefore,
$\frac{A B}{D F}=\frac{A C}{D E}$
$\frac{5}{7.5}=\frac{8}{D E}$
$D E=\frac{8 \times 7.5}{5}$
$=12 \mathrm{~cm}$
Therefore,
$D E=12 \mathrm{~cm}, \angle F=100^{\circ}$
Related Articles
- Choose the correct answer from the given four options:In below figure, two line segments \( \mathrm{AC} \) and \( \mathrm{BD} \) intersect each other at the point \( \mathrm{P} \) such that \( \mathrm{PA}=6 \mathrm{~cm}, \mathrm{~PB}=3 \mathrm{~cm}, \mathrm{PC}=2.5 \mathrm{~cm}, \mathrm{PD}=5 \mathrm{~cm}, \angle \mathrm{APB}=50^{\circ} \) and \( \angle \mathrm{CDP}=30^{\circ} \). Then, \( \angle \mathrm{PBA} \) is equal to(A) \( 50^{\circ} \)(B) \( 30^{\circ} \)(C) \( 60^{\circ} \)(D) \( 100^{\circ} \)"
- Name the types of following triangles:(a) Triangle with lengths of sides \( 7 \mathrm{~cm}, 8 \mathrm{~cm} \) and \( 9 \mathrm{~cm} \).(b) \( \triangle \mathrm{ABC} \) with \( \mathrm{AB}=8.7 \mathrm{~cm}, \mathrm{AC}=7 \mathrm{~cm} \) and \( \mathrm{BC}=6 \mathrm{~cm} \).(c) \( \triangle \mathrm{PQR} \) such that \( \mathrm{PQ}=\mathrm{QR}=\mathrm{PR}=5 \mathrm{~cm} \).(d) \( \triangle \mathrm{DEF} \) with \( \mathrm{m} \angle \mathrm{D}=90^{\circ} \)(e) \( \triangle \mathrm{XYZ} \) with \( \mathrm{m} \angle \mathrm{Y}=90^{\circ} \) and \( \mathrm{XY}=\mathrm{YZ} \).(f) \( \Delta \mathrm{LMN} \) with \( \mathrm{m} \angle \mathrm{L}=30^{\circ}, \mathrm{m} \angle \mathrm{M}=70^{\circ} \) and \( \mathrm{m} \angle \mathrm{N}=80^{\circ} \).
- Construct a triangle \( \mathrm{ABC} \) in which \( \mathrm{BC}=8 \mathrm{~cm}, \angle \mathrm{B}=45^{\circ} \) and \( \mathrm{AB}-\mathrm{AC}=3.5 \mathrm{~cm} \).
- Construct a triangle \( \mathrm{ABC} \) in which \( \mathrm{BC}=7 \mathrm{~cm}, \angle \mathrm{B}=75^{\circ} \) and \( \mathrm{AB}+\mathrm{AC}=13 \mathrm{~cm} \).
- Construct a triangle \( \mathrm{XYZ} \) in which \( \angle \mathrm{Y}=30^{\circ}, \angle \mathrm{Z}=90^{\circ} \) and \( \mathrm{XY}+\mathrm{YZ}+\mathrm{ZX}=11 \mathrm{~cm} \).
- In triangles \( \mathrm{PQR} \) and \( \mathrm{MST}, \angle \mathrm{P}=55^{\circ}, \angle \mathrm{Q}=25^{\circ}, \angle \mathrm{M}=100^{\circ} \) and \( \angle \mathrm{S}=25^{\circ} \). Is \( \triangle \mathrm{QPR} \sim \triangle \mathrm{TSM} \) ? Why?
- If \( \Delta \mathrm{ABC} \sim \Delta \mathrm{DEF}, \mathrm{AB}=4 \mathrm{~cm}, \mathrm{DE}=6 \mathrm{~cm}, \mathrm{EF}=9 \mathrm{~cm} \) and \( \mathrm{FD}=12 \mathrm{~cm} \), find the perimeter of \( \triangle \mathrm{ABC} \).
- In \( \triangle \mathrm{ABC}, \angle \mathrm{C}=90^{\circ}, \mathrm{AB}=12.5 \) and \( \mathrm{BC}=12 \). Find \( \mathrm{AC} \).
- Choose the correct answer from the given four options:If in triangles \( \mathrm{ABC} \) and \( \mathrm{DEF}, \frac{\mathrm{AB}}{\mathrm{DE}}=\frac{\mathrm{BC}}{\mathrm{FD}} \), then they will be similar, when(A) \( \angle \mathrm{B}=\angle \mathrm{E} \)(B) \( \angle \mathrm{A}=\angle \mathrm{D} \)(C) \( \angle \mathrm{B}=\angle \mathrm{D} \)(D) \( \angle \mathrm{A}=\angle \mathrm{F} \)
- In figure, if \( \angle \mathrm{A}=\angle \mathrm{C}, \mathrm{AB}=6 \mathrm{~cm}, \mathrm{BP}=15 \mathrm{~cm} \), \( \mathrm{AP}=12 \mathrm{~cm} \) and \( \mathrm{CP}=4 \mathrm{~cm} \), then find the lengths of \( \mathrm{PD} \) and CD."
- Construct a triangle \( \mathrm{PQR} \) in which \( \mathrm{QR}=6 \mathrm{~cm}, \angle \mathrm{Q}=60^{\circ} \) and \( \mathrm{PR}-\mathrm{PQ}=2 \mathrm{~cm} \).
- 10. Construct \( \triangle \mathrm{PQR} \) with \( \mathrm{PQ}=4.5 \mathrm{~cm}, \angle \mathrm{P}=60^{\circ} \) and \( \mathrm{PR}=4.5 \mathrm{~cm} . \) Measure \( \angle \mathrm{Q} \) and \( \angle \mathrm{R} \). What type of a triangle is it?
- \( \triangle \mathrm{ABC} \sim \triangle \mathrm{QPR} . \) If \( \angle \mathrm{A}+\angle \mathrm{B}=130^{\circ} \) and \( \angle B+\angle C=125^{\circ} \), find \( \angle Q \).
- \( \triangle \mathrm{ABC} \sim \triangle \mathrm{PQR} . \quad \) If \( \quad \mathrm{AB}+\mathrm{BC}=12 \mathrm{~cm} \) \( \mathrm{PQ}+\mathrm{QR}=15 \mathrm{~cm} \) and \( \mathrm{AC}=8 \mathrm{~cm} \), find \( \mathrm{PR} \).
- In \( \triangle \mathrm{ABC}, \angle \mathrm{B}=90^{\circ} \) and \( \mathrm{BM} \) is an altitude. If \( \mathrm{BM}=\sqrt{30} \) and \( \mathrm{CM}=3 \), find \( \mathrm{AC} \).
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies