Sides of triangles are given below. Determine which of them are right triangles. In case of a right triangle,write the length of its hypotenuse.
$50 \text{ cm}, 80 \text{ cm}, 100 \text{ cm}$

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(NONE) Given that the sides of the triangle are $50 \text{ cm}, 80 \text{ cm},$ and $100 \text{ cm}.$
To check if it is a right-angled triangle,we apply the converse of the Pythagoras theorem,which states that in a triangle,if the square of the length of the longest side is equal to the sum of the squares of the lengths of the other two sides,then it is a right-angled triangle.
Calculate the squares of the sides:
$50^2 = 2500$
$80^2 = 6400$
$100^2 = 10000$
Now,check the sum of the squares of the two smaller sides:
$50^2 + 80^2 = 2500 + 6400 = 8900$
Comparing this with the square of the longest side:
$8900 \neq 10000$
Since $50^2 + 80^2 \neq 100^2$,the given triangle does not satisfy the Pythagoras theorem.
Therefore,the given triangle is not a right-angled triangle.

Explore More

Similar Questions

Prove that if in a triangle the square of one side is equal to the sum of the squares of the other two sides,then the angle opposite the first side is a right angle.

Difficult
View Solution

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude. If $AM = x + 7$,$BM = x + 2$,and $CM = x$,find the value of $x$.

In the figure,$PS$ is the bisector of $\angle QPR$ of $\Delta PQR$. Prove that $\frac{QS}{SR} = \frac{PQ}{PR}$.

Difficult
View Solution

In $\Delta PQR$,$P-X-Q$,$P-Y-R$ and $\overline{XY} \parallel \overline{QR}$. If $PX = 3$,$PQ = 8$ and $PY = 4.2$,find $YR$.

In $\Delta PQR$,$m\angle P = 90^{\circ}$ and $\overline{PM}$ is an altitude. If $PQ = \sqrt{20}$ and $QM = 4$,then $RM = \ldots \ldots .$

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