Write the measures of the sides of $\Delta PQR$ in ascending order,given that $\angle P = 93^{\circ}$ and $\angle R = 55^{\circ}$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(A) In $\Delta PQR$,the sum of all angles is $180^{\circ}$.
$\angle P + \angle Q + \angle R = 180^{\circ}$
$93^{\circ} + \angle Q + 55^{\circ} = 180^{\circ}$
$148^{\circ} + \angle Q = 180^{\circ}$
$\angle Q = 180^{\circ} - 148^{\circ} = 32^{\circ}$.
Since the side opposite to the smallest angle is the shortest and the side opposite to the largest angle is the longest,we compare the angles: $\angle Q (32^{\circ}) < \angle R (55^{\circ}) < \angle P (93^{\circ})$.
Therefore,the sides in ascending order are: $PR < PQ < QR$.

Explore More

Similar Questions

$ABCD$ is a quadrilateral such that $AB = AD$ and $CB = CD$. Prove that $AC$ is the perpendicular bisector of $BD$.

Difficult
View Solution

If $\Delta ABC \cong \Delta YZX,$ then in $\Delta XYZ,$ which side is equal to side $AB$?

In $\Delta PQR$,$\angle Q = \angle R$ and $PQ = 6.5 \, cm$,then find $PR$. (in $, cm$)

In $\Delta PQR$,$PQ = PR$. Prove that $\angle R = \angle Q$.

$AD$ is a median of the triangle $ABC$. Is it true that $AB + BC + CA > 2AD$? Give reason for your answer.

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