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: $PQ = 15, QR = 17, PR = 8$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(D) In $\Delta PQR$,the side lengths are $PQ = 15$,$QR = 17$,and $PR = 8$.
To determine if it is a right-angled triangle,we check the converse of the Pythagoras theorem.
The longest side is $QR = 17$.
Calculate the square of the longest side: $QR^2 = 17^2 = 289$.
Calculate the sum of the squares of the other two sides: $PQ^2 + PR^2 = 15^2 + 8^2 = 225 + 64 = 289$.
Since $PQ^2 + PR^2 = QR^2$,the triangle satisfies the Pythagoras theorem.
Therefore,$\Delta PQR$ is a right-angled triangle,and the angle opposite to the hypotenuse $QR$ is $\angle P = 90^\circ$.

Explore More

Similar Questions

Point $O$ lies in the interior of $\Delta ABC$. The bisectors of $\angle AOB, \angle BOC$ and $\angle COA$ intersect $\overline{AB}, \overline{BC}$ and $\overline{CA}$ at $D, E$ and $F$ respectively. Prove that $AD \times BE \times CF = DB \times EC \times FA$.

Difficult
View Solution

$A$ $17 \, m$ long ladder leans on a wall such that its lower end rests $8 \, m$ away from the base of the wall. Then,its upper end reaches to the height of $\ldots \ldots \ldots \, m$ on the wall.

In the given figure,if $AB \parallel DC$ and $AC$ and $PQ$ intersect each other at the point $O$,prove that $OA \cdot CQ = OC \cdot AP$.

In $\Delta ABC$,$m\angle B = 90^{\circ}$. If $AB : BC = 3 : 4$,find $AB : AC$.

In $\Delta ABC$,$m\angle B = 90^{\circ}$ and $\overline{BM}$ is a median. If $AB = 15$ and $BM = 12.5$,find $BC$.

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