Recall the Pythagorean Theorem, which is used to find the length of the hypotenuse.

For any triangle with leg lengths of $\displaystyle a$ and $\displaystyle b$,

$\displaystyle \text{Hypotenuse}^2=a^2+b^2$

Take the square root of both sides to find the length of the hypotenuse.

$\displaystyle \text{Hypotenuse}=\sqrt{a^2+b^2}$

Plug in the given values to find the length of the hypotenuse.

$\displaystyle \text{Hypotenuse}=\sqrt{7^2 + 4^2}=\sqrt{65}$

By the Pythagorean Theorem, which says $\displaystyle a^2+b^2=c^2$. $\displaystyle c$ being the hypotenuse, or $\displaystyle x$ in this problem. 

$\displaystyle x^{2} = 6^{2} + 9^{2}$

$\displaystyle x^{2} = 36 + 81$

$\displaystyle x^{2} = 117$

$\displaystyle x =\sqrt{ 117}$

Simply

$\displaystyle \sqrt{ 9} \cdot \sqrt{ 13}$

$\displaystyle 3 \sqrt{ 13}$

Recall the Pythagorean Theorem, which is used to find the length of the hypotenuse.

For any triangle with leg lengths of $\displaystyle a$ and $\displaystyle b$,

$\displaystyle \text{Hypotenuse}^2=a^2+b^2$

Take the square root of both sides to find the length of the hypotenuse.

$\displaystyle \text{Hypotenuse}=\sqrt{a^2+b^2}$

Plug in the given values to find the length of the hypotenuse.

$\displaystyle \text{Hypotenuse}=\sqrt{10^2 + 4^2}=\sqrt{116}$

Simply:

$\displaystyle \sqrt{4}\cdot\sqrt{29}$

$\displaystyle 2\sqrt{29}$

The provided triangle is a right triangle. We know this because the angle marker in the left corner of the triangle indicates that the triangle possesses a right or $\displaystyle 90^\circ$ angle. When a triangle includes a right angle, the triangle is said to be a "right triangle." 

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

$\displaystyle a^2+b^2=c^2$

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

$\displaystyle 9^2+8^2=c^2$

$\displaystyle 81+64=c^2$

$\displaystyle 145=c^2$

$\displaystyle \sqrt{145}=\sqrt{c^2}$

$\displaystyle 12.04=c$

or

$\displaystyle c=12$

The provided triangle is a right triangle. We know this because the angle marker in the left corner of the triangle indicates that the triangle possesses a right or $\displaystyle 90^\circ$ angle. When a triangle includes a right angle, the triangle is said to be a "right triangle." 

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

$\displaystyle a^2+b^2=c^2$

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

$\displaystyle 12^2+35^2=c^2$

$\displaystyle 144+1\textup,225=c^2$

$\displaystyle 1\textup,369=c^2$

$\displaystyle \sqrt{1\textup,369}=\sqrt{c^2}$

$\displaystyle 37=c$

The provided triangle is a right triangle. We know this because the angle marker in the left corner of the triangle indicates that the triangle possesses a right or $\displaystyle 90^\circ$ angle. When a triangle includes a right angle, the triangle is said to be a "right triangle." 

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

$\displaystyle a^2+b^2=c^2$

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

$\displaystyle 8^2+15^2=c^2$

$\displaystyle 64+225=c^2$

$\displaystyle 289=c^2$

$\displaystyle \sqrt{289}=\sqrt{c^2}$

$\displaystyle 17=c$

The provided triangle is a right triangle. We know this because the angle marker in the left corner of the triangle indicates that the triangle possesses a right or $\displaystyle 90^\circ$ angle. When a triangle includes a right angle, the triangle is said to be a "right triangle." 

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

$\displaystyle a^2+b^2=c^2$

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

$\displaystyle 24^2+32^2=c^2$

$\displaystyle 576+1\textup,024=c^2$

$\displaystyle 1\textup,600=c^2$

$\displaystyle \sqrt{1\textup,600}=\sqrt{c^2}$

$\displaystyle 40$

The provided triangle is a right triangle. We know this because the angle marker in the left corner of the triangle indicates that the triangle possesses a right or $\displaystyle 90^\circ$ angle. When a triangle includes a right angle, the triangle is said to be a "right triangle." 

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

$\displaystyle a^2+b^2=c^2$

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

$\displaystyle 72^2+21^2=c^2$

$\displaystyle 5\textup,184+441=c^2$

$\displaystyle 5\textup,625=c^2$

$\displaystyle \sqrt{5\textup,625}=\sqrt{c^2}$

$\displaystyle 75=c$

The provided triangle is a right triangle. We know this because the angle marker in the left corner of the triangle indicates that the triangle possesses a right or $\displaystyle 90^\circ$ angle. When a triangle includes a right angle, the triangle is said to be a "right triangle." 

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

$\displaystyle a^2+b^2=c^2$

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

$\displaystyle 12^2+5^2=c^2$

$\displaystyle 144+25=c^2$

$\displaystyle 169=c^2$

$\displaystyle \sqrt{169}=\sqrt{c^2}$

$\displaystyle 13=c$

The provided triangle is a right triangle. We know this because the angle marker in the left corner of the triangle indicates that the triangle possesses a right or $\displaystyle 90^\circ$ angle. When a triangle includes a right angle, the triangle is said to be a "right triangle." 

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

$\displaystyle a^2+b^2=c^2$

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

$\displaystyle 16^2+12^2=c^2$

$\displaystyle 256+144=c^2$

$\displaystyle 400=c^2$

$\displaystyle \sqrt{400}=\sqrt{c^2}$

$\displaystyle 20=c$