This is solving for the hypotenuse of a triangle. Using the Pythagorean Theorem, which says that \(\displaystyle a^2+b^2=c^2\) 

 \(\displaystyle 15^2 + 20^2 = c^2\) 

\(\displaystyle 225+400=c^2\)

\(\displaystyle 625=c^2\)

\(\displaystyle 25=c\)

Notice that the diagonal line from the problem could be the hypotenuse of a right triangle. If we add two more lines, then we can create a closed figure in the shape of a triangle:

Let's use the Pythagorean Theorem to calculate the length of the line that represents the hypotenuse of a right triangle. The Pythagorean Theorem states that for right triangles:

\(\displaystyle a^2+b^2=c^2\)

In this equation:

\(\displaystyle a \textup{ and }b=\textup{legs}\)

\(\displaystyle c=\textup{hypotenuse}\)

We can count the number of units on the coordinate plane that were used to create the legs of our drawn triangle. Afterwards, we can use the Pythagorean Theorem to solve for the length of the hypotenuse, or the original diagonal line. 

In order to solve for this problem we want to substitute in the known side lengths for the triangle's legs:

\(\displaystyle 4^2+4^2=c^2\)

\(\displaystyle 16+16=c^2\)

\(\displaystyle 32=c^2\)

\(\displaystyle \sqrt{32}=\sqrt{c^2}\)

\(\displaystyle 5.7=c\)

Notice that the diagonal line from the problem could be the hypotenuse of a right triangle. If we add two more lines, then we can create a closed figure in the shape of a triangle:

Let's use the Pythagorean Theorem to calculate the length of the line that represents the hypotenuse of a right triangle. The Pythagorean Theorem states that for right triangles:

\(\displaystyle a^2+b^2=c^2\)

In this equation:

\(\displaystyle a \textup{ and }b=\textup{legs}\)

\(\displaystyle c=\textup{hypotenuse}\)

We can count the number of units on the coordinate plane that were used to create the legs of our drawn triangle. Afterwards, we can use the Pythagorean Theorem to solve for the length of the hypotenuse, or the original diagonal line. 

In order to solve for this problem we want to substitute in the known side lengths for the triangle's legs:

\(\displaystyle 7^2+7^2=c^2\)

\(\displaystyle 49+49=c^2\)

\(\displaystyle 98=c^2\)

\(\displaystyle \sqrt{98}=\sqrt{c^2}\)

\(\displaystyle 9.9=c\)

Notice that the diagonal line from the problem could be the hypotenuse of a right triangle. If we add two more lines, then we can create a closed figure in the shape of a triangle:

Let's use the Pythagorean Theorem to calculate the length of the line that represents the hypotenuse of a right triangle. The Pythagorean Theorem states that for right triangles:

\(\displaystyle a^2+b^2=c^2\)

In this equation:

\(\displaystyle a \textup{ and }b=\textup{legs}\)

\(\displaystyle c=\textup{hypotenuse}\)

We can count the number of units on the coordinate plane that were used to create the legs of our drawn triangle. Afterwards, we can use the Pythagorean Theorem to solve for the length of the hypotenuse, or the original diagonal line. 

In order to solve for this problem we want to substitute in the known side lengths for the triangle's legs:

\(\displaystyle 4^2+11^2=c^2\)

\(\displaystyle 16+121=c^2\)

\(\displaystyle 137=c^2\)

\(\displaystyle \sqrt{137}=\sqrt{c^2}\)

\(\displaystyle 11.7=c\)

Notice that the diagonal line from the problem could be the hypotenuse of a right triangle. If we add two more lines, then we can create a closed figure in the shape of a triangle:

Let's use the Pythagorean Theorem to calculate the length of the line that represents the hypotenuse of a right triangle. The Pythagorean Theorem states that for right triangles:

\(\displaystyle a^2+b^2=c^2\)

In this equation:

\(\displaystyle a \textup{ and }b=\textup{legs}\)

\(\displaystyle c=\textup{hypotenuse}\)

We can count the number of units on the coordinate plane that were used to create the legs of our drawn triangle. Afterwards, we can use the Pythagorean Theorem to solve for the length of the hypotenuse, or the original diagonal line. 

In order to solve for this problem we want to substitute in the known side lengths for the triangle's legs:

\(\displaystyle 5^2+10^2=c^2\)

\(\displaystyle 25+100=c^2\)

\(\displaystyle 125=c^2\)

\(\displaystyle \sqrt{125}=\sqrt{c^2}\)

\(\displaystyle 11.2=c\)

Notice that the diagonal line from the problem could be the hypotenuse of a right triangle. If we add two more lines, then we can create a closed figure in the shape of a triangle:

Let's use the Pythagorean Theorem to calculate the length of the line that represents the hypotenuse of a right triangle. The Pythagorean Theorem states that for right triangles:

\(\displaystyle a^2+b^2=c^2\)

In this equation:

\(\displaystyle a \textup{ and }b=\textup{legs}\)

\(\displaystyle c=\textup{hypotenuse}\)

We can count the number of units on the coordinate plane that were used to create the legs of our drawn triangle. Afterwards, we can use the Pythagorean Theorem to solve for the length of the hypotenuse, or the original diagonal line. 

In order to solve for this problem we want to substitute in the known side lengths for the triangle's legs:

\(\displaystyle 3^2+5^2=c^2\)

\(\displaystyle 9+25=c^2\)

\(\displaystyle 34=c^2\)

\(\displaystyle \sqrt{34}=\sqrt{c^2}\)

\(\displaystyle 5.8=c\)

Notice that the diagonal line from the problem could be the hypotenuse of a right triangle. If we add two more lines, then we can create a closed figure in the shape of a triangle:

Let's use the Pythagorean Theorem to calculate the length of the line that represents the hypotenuse of a right triangle. The Pythagorean Theorem states that for right triangles:

\(\displaystyle a^2+b^2=c^2\)

In this equation:

\(\displaystyle a \textup{ and }b=\textup{legs}\)

\(\displaystyle c=\textup{hypotenuse}\)

We can count the number of units on the coordinate plane that were used to create the legs of our drawn triangle. Afterwards, we can use the Pythagorean Theorem to solve for the length of the hypotenuse, or the original diagonal line. 

In order to solve for this problem we want to substitute in the known side lengths for the triangle's legs:

\(\displaystyle 6^2+5^2=c^2\)

\(\displaystyle 36+25=c^2\)

\(\displaystyle 61=c^2\)

\(\displaystyle \sqrt{61}=\sqrt{c^2}\)

\(\displaystyle 7.8=c\)

Notice that the diagonal line from the problem could be the hypotenuse of a right triangle. If we add two more lines, then we can create a closed figure in the shape of a triangle:

Let's use the Pythagorean Theorem to calculate the length of the line that represents the hypotenuse of a right triangle. The Pythagorean Theorem states that for right triangles:

\(\displaystyle a^2+b^2=c^2\)

In this equation:

\(\displaystyle a \textup{ and }b=\textup{legs}\)

\(\displaystyle c=\textup{hypotenuse}\)

We can count the number of units on the coordinate plane that were used to create the legs of our drawn triangle. Afterwards, we can use the Pythagorean Theorem to solve for the length of the hypotenuse, or the original diagonal line. 

In order to solve for this problem we want to substitute in the known side lengths for the triangle's legs:

\(\displaystyle 10^2+7^2=c^2\)

\(\displaystyle 100+49=c^2\)

\(\displaystyle 149=c^2\)

\(\displaystyle \sqrt{149}=\sqrt{c^2}\)

\(\displaystyle 12.2=c\)

Notice that the diagonal line from the problem could be the hypotenuse of a right triangle. If we add two more lines, then we can create a closed figure in the shape of a triangle:

Let's use the Pythagorean Theorem to calculate the length of the line that represents the hypotenuse of a right triangle. The Pythagorean Theorem states that for right triangles:

\(\displaystyle a^2+b^2=c^2\)

In this equation:

\(\displaystyle a \textup{ and }b=\textup{legs}\)

\(\displaystyle c=\textup{hypotenuse}\)

We can count the number of units on the coordinate plane that were used to create the legs of our drawn triangle. Afterwards, we can use the Pythagorean Theorem to solve for the length of the hypotenuse, or the original diagonal line. 

In order to solve for this problem we want to substitute in the known side lengths for the triangle's legs:

\(\displaystyle 6^2+5^2=c^2\)

\(\displaystyle 36+25=c^2\)

\(\displaystyle 61=c^2\)

\(\displaystyle \sqrt{61}=\sqrt{c^2}\)

\(\displaystyle 7.8=c\)

Notice that the diagonal line from the problem could be the hypotenuse of a right triangle. If we add two more lines, then we can create a closed figure in the shape of a triangle:

Let's use the Pythagorean Theorem to calculate the length of the line that represents the hypotenuse of a right triangle. The Pythagorean Theorem states that for right triangles:

\(\displaystyle a^2+b^2=c^2\)

In this equation:

\(\displaystyle a \textup{ and }b=\textup{legs}\)

\(\displaystyle c=\textup{hypotenuse}\)

We can count the number of units on the coordinate plane that were used to create the legs of our drawn triangle. Afterwards, we can use the Pythagorean Theorem to solve for the length of the hypotenuse, or the original diagonal line. 

In order to solve for this problem we want to substitute in the known side lengths for the triangle's legs:

\(\displaystyle 4^2+5^2=c^2\)

\(\displaystyle 16+25=c^2\)

\(\displaystyle 41=c^2\)

\(\displaystyle \sqrt{41}=\sqrt{c^2}\)

\(\displaystyle 6.4=c\)