Write True or False and give reasons for your answer.
By geometrical construction,it is possible to divide a line segment in the ratio $\sqrt{3}: \frac{1}{\sqrt{3}}$.
By geometrical construction,it is possible to divide a line segment in the ratio $\sqrt{3}: \frac{1}{\sqrt{3}}$.
(A) True.
Given ratio $= \sqrt{3} : \frac{1}{\sqrt{3}}$.
To simplify this ratio,multiply both terms by $\sqrt{3}$:
$\sqrt{3} \times \sqrt{3} : \frac{1}{\sqrt{3}} \times \sqrt{3} = 3 : 1$.
Since $3 : 1$ is a ratio of two positive integers,it is always possible to divide a line segment in this ratio using a ruler and compass by constructing $3 + 1 = 4$ equal parts on an auxiliary ray.
Therefore,the statement is True.
Given ratio $= \sqrt{3} : \frac{1}{\sqrt{3}}$.
To simplify this ratio,multiply both terms by $\sqrt{3}$:
$\sqrt{3} \times \sqrt{3} : \frac{1}{\sqrt{3}} \times \sqrt{3} = 3 : 1$.
Since $3 : 1$ is a ratio of two positive integers,it is always possible to divide a line segment in this ratio using a ruler and compass by constructing $3 + 1 = 4$ equal parts on an auxiliary ray.
Therefore,the statement is True.
Explore More
Similar Questions
To construct a triangle similar to a given $\triangle ABC$ with its sides being $\frac{8}{5}$ of the corresponding sides of $\triangle ABC$,a ray $BX$ is drawn such that $\angle CBX$ is an acute angle and $X$ is on the opposite side of $A$ with respect to $BC$. The minimum number of points to be located at equal distances on ray $BX$ is
Medium
View SolutionTo divide a line segment $AB$ in the ratio $5: 6,$ draw a ray $AX$ such that $\angle BAX$ is an acute angle,then draw a ray $BY$ parallel to $AX$ and the points $A_{1}, A_{2}, A_{3}, \ldots$ and $B_{1}, B_{2}, B_{3}, \ldots$ are located at equal distances on ray $AX$ and $BY,$ respectively. Then the points joined are
Difficult
View SolutionDraw $\odot( P , 3 \, cm )$ and a diameter $\overline{ AB }$ in it. Take points $X$ and $Y$ such that $X - A - B$ and $A - B - Y$ where $PX = PY = 7 \, cm$. From $X$ and $Y$,draw tangents to $\odot( P , 3 \, cm )$. Write the steps of construction.
Difficult
View SolutionDraw $\overline{PQ}$ of length $8.5 \text{ cm}$ and obtain point $X$ on $\overline{PQ}$ such that $PX : XQ = 4 : 7$. Write the steps of construction.
Difficult
View SolutionTo draw a pair of tangents to a circle which are inclined to each other at an angle of $35^{\circ},$ it is required to draw tangents at the end points of those two radii of the circle,the angle between which is (in $^{\circ}$)
Easy
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