Construct a right triangle whose base is $6\,cm$ and the sum of its hypotenuse and the other side is $12\,cm$. Write the steps of construction.
(N/A) $1$. Draw a line segment $AB = 6\,cm$ as the base.
$2$. At point $B$,construct an angle of $90^\circ$ using a compass.
$3$. From the ray $BX$ (making $90^\circ$ with $AB$),cut off a line segment $BD = 12\,cm$.
$4$. Join $AD$.
$5$. Draw the perpendicular bisector of $AD$,which intersects $BD$ at point $C$.
$6$. Join $AC$. Thus,$\triangle ABC$ is the required right-angled triangle where $BC + AC = 12\,cm$ and $AB = 6\,cm$.
$2$. At point $B$,construct an angle of $90^\circ$ using a compass.
$3$. From the ray $BX$ (making $90^\circ$ with $AB$),cut off a line segment $BD = 12\,cm$.
$4$. Join $AD$.
$5$. Draw the perpendicular bisector of $AD$,which intersects $BD$ at point $C$.
$6$. Join $AC$. Thus,$\triangle ABC$ is the required right-angled triangle where $BC + AC = 12\,cm$ and $AB = 6\,cm$.
Explore More
Similar Questions
Write True or False and give reasons for your answer.
$A$ triangle $ABC$ can be constructed in which $AB = 5 \, cm$,$\angle A = 45^{\circ}$ and $BC + AC = 5 \, cm$.
$A$ triangle $ABC$ can be constructed in which $AB = 5 \, cm$,$\angle A = 45^{\circ}$ and $BC + AC = 5 \, cm$.
Easy
View SolutionConstruct a right triangle whose base is $3\,cm$ and the sum of its hypotenuse and the other side is $9\,cm$. Write the steps of construction.
Medium
View SolutionConstruct a triangle $PQR$,in which $QR = 9\, cm$,$\angle Q = 60^{\circ}$ and $PR - PQ = 3\, cm$.
Difficult
View SolutionWrite True or False and give reasons for your answer.
$A$ triangle $ABC$ can be constructed in which $BC = 6 \, cm$,$\angle C = 30^{\circ}$ and $AC - AB = 4 \, cm$.
$A$ triangle $ABC$ can be constructed in which $BC = 6 \, cm$,$\angle C = 30^{\circ}$ and $AC - AB = 4 \, cm$.
Easy
View SolutionDraw an obtuse angle and bisect it. Write the steps of construction.
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo