Below are given the measures of sides $\overline{PQ}$,$\overline{QR}$ and $\overline{PR}$ of $\Delta PQR$. In each case,determine whether $\Delta PQR$ is a right-angled triangle or not. If it is a right-angled triangle,state which angle is a right angle: $PQ = 7, QR = 24, PR = 25$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(D) In $\Delta PQR$,the side lengths are $PQ = 7$,$QR = 24$,and $PR = 25$.
The longest side is $PR = 25$.
Calculate the square of the longest side:
$PR^2 = 25^2 = 625$
Calculate the sum of the squares of the other two sides:
$PQ^2 + QR^2 = 7^2 + 24^2 = 49 + 576 = 625$
Since $PQ^2 + QR^2 = PR^2$,the triangle satisfies the converse of the Pythagoras theorem.
Therefore,$\Delta PQR$ is a right-angled triangle,and the angle opposite to the hypotenuse $PR$,which is $\angle Q$,is the right angle.

Explore More

Similar Questions

If in the figure, $O$ is the point of intersection of two chords $AB$ and $CD$ such that $OB = OD$, then triangles $OAC$ and $ODB$ are

In rectangle $ABCD$,$AB^{2} + BC^{2} + CD^{2} + DA^{2} = 338$,then $AC = \ldots$

Difficult
View Solution

In $\Delta PQR$,the bisector of $\angle P$ intersects $\overline{QR}$ at $S$. If $PQ : PR = 5 : 4$ and $SR = 5.6 \text{ cm}$,then $QR = \ldots \text{ cm}$.

$\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow PQR$. If $AB = 4, BC = 8, AC = 10$ and $PR = 15$,then the perimeter of $\Delta PQR = \dots$

In quadrilateral $ABCD$,$\overline{AB} \parallel \overline{CD}$ and $\overline{AC} \cap \overline{BD} = \{O\}$. If $OA = 3x - 19$,$OB = x - 4$,$OC = x - 3$,and $OD = 4$,find the value of $x$.

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