Pythagoras Theorem

A congruent side of an isosceles right-angled triangle is $7 \mathrm{cm}$ ,Find its perimeter.

In the given figure, $∆PQR$ is right-angled at $Q$ and point $S$ and $T$ trisect side $QR$. Prove that $8P{T}^2=3P{R}^2+5P{S}^2$

In $△ABC, AB= 9 cm, BC = 40 cm, AC = 41 cm .$ . State whether $△ ABC$ is a right-angled triangle or not ? Write reason

What is $30°-60°-90°$ theorem?

In right-angled $△ABC$, $BD\perp AC$. If $AD=4, DC=9$, then find $BD$.

The area of a right-angled triangle is $40$ times its base. What is its height?

Height and base of a right triangle are $24 \mathrm{cm}$ and $18 \mathrm{cm}$, find the length of its hypotenuse.

In the given figure, $\angle DFE=90°, FG\perp ED$. If $GD=8, FG=12$, find $EG$.

In the given figure, $\angle QPR=90°, seg PM\perp seg QR$, $PM=10, QM=8$, find $QR$.

In the given figure, $\angle MNP=90°, seg NQ\perp seg MP, MQ=9, QP=4$, find $NQ$.

In a right-angled isosceles triangle, the measure of equal angles will be _____$°$.

The base and height of a right-angled triangle are $5\text{cm} \text{and} 12\text{cm}$ respectively. Find the third side and draw the right-angled triangle.

The base and height of a right-angled triangle are $3\text{cm} \text{and} 4\text{cm}$ respectively. Find the third side and draw the right-angled triangle.

If the Perimeter of the following triangle is $\frac{6+2\sqrt{k}}{\sqrt{k}}$ then the value of $k=$_____.

The length and breadth of the screen of an LED-TV are $24$ inches and $18$ inches. Find the length of its diagonal in inches.

From the figure,

If $TA=3 \mathrm{cm}$ and $OT=6 \mathrm{cm},$ find $TG$ in $\mathrm{cm}$.

A vertical tree is broken by the wind at a height of $6 \mathrm{m}$ from its foot and its top touches the ground at a distance of $8 \mathrm{m}$ from the foot of the tree. Calculate the distance (in $\mathrm{m}$) between the top of the tree before breaking and the point at which the tip of the tree touches the ground, after it breaks (to the nearest whole number).

Srivani walks$12 \mathrm{m}$ due East and turns left and walks another $5 \mathrm{m}$, how far (in $\mathrm{m}$) is she from the place she started?

Find the perimeter (in $\mathrm{cm}$) of a square whose diagonal is $13\sqrt{2} \mathrm{cm}$.

In $△ABC$, segment $AP$ is a median. If $BC=18, A{B}^2+A{C}^2= 260$, then find the length of $AP$.