Is it possible to construct a triangle with lengths of its sides as $9 \, cm$,$7 \, cm$,and $17 \, cm$? Give reason for your answer.
(N/A) No,it is not possible to construct a triangle with side lengths $9 \, cm$,$7 \, cm$,and $17 \, cm$.
According to the triangle inequality theorem,the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Here,the sum of the two smaller sides is:
$9 \, cm + 7 \, cm = 16 \, cm$
Since $16 \, cm < 17 \, cm$,the sum of the two sides is not greater than the third side.
Therefore,a triangle cannot be formed with these side lengths.
According to the triangle inequality theorem,the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Here,the sum of the two smaller sides is:
$9 \, cm + 7 \, cm = 16 \, cm$
Since $16 \, cm < 17 \, cm$,the sum of the two sides is not greater than the third side.
Therefore,a triangle cannot be formed with these side lengths.
Explore More
Similar Questions
$\angle ACD$ is an exterior angle of $\Delta ABC$. If $AB = AC$ and $\angle B = 70^{\circ}$,then $\angle ACD = \dots$ (in $^{\circ}$)
Medium
View Solution$AD$ is a median of the triangle $ABC$. Is it true that $AB + BC + CA > 2AD$? Give reason for your answer.
Medium
View Solution$S$ is any point on side $QR$ of a $\triangle PQR$. Show that: $PQ + QR + RP > 2 \, PS$.
Medium
View SolutionIn triangles $ABC$ and $PQR$,$AB = AC$,$\angle C = \angle P$ and $\angle B = \angle Q$. The two triangles are
Medium
View SolutionThe difference of any two sides of a triangle is $\ldots \ldots \ldots$ than the third side.
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