Construct $\Delta ABC$ in which $\angle B = 30^{\circ}$,$\angle C = 90^{\circ}$ and $AB + BC + CA = 14 \, cm$. Write the steps of construction.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) Steps of construction:
$1$. Draw a line segment $XY = 14 \, cm$ which is equal to the perimeter of the triangle $(AB + BC + CA)$.
$2$. Construct $\angle LXY = 30^{\circ}$ at point $X$ and $\angle MYX = 90^{\circ}$ at point $Y$.
$3$. Bisect $\angle LXY$ and $\angle MYX$. Let the bisectors intersect at point $A$.
$4$. Draw the perpendicular bisector of $AX$ to intersect $XY$ at $B$.
$5$. Draw the perpendicular bisector of $AY$ to intersect $XY$ at $C$.
$6$. Join $AB$ and $AC$. Thus,$\Delta ABC$ is the required triangle.

Explore More

Similar Questions

Construct $\Delta PQR$ in which $QR = 4\,cm$,$\angle Q = 45^{\circ}$ and $PQ + PR = 8\,cm$. Write the steps of construction.

Construct a triangle with a perimeter of $10.4 \, cm$ and two base angles of $45^{\circ}$ and $120^{\circ}$. Provide the justification for the construction.

Draw an angle of $110^{\circ}$ with the help of a protractor and bisect it. Measure each angle.

Construct an angle of $45^{\circ}$ at the initial point of a given ray and justify the construction.

Difficult
View Solution

Draw a line segment $AB$ of $4 \,cm$ in length. Draw a line perpendicular to $AB$ through $A$ and $B$,respectively. Are these lines parallel?

Difficult
View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo