Question

How do you find the missing side a given 12mm, 15mm right triangle using the Pythagorean Theorem?

Answer 1

Hint: This question belongs to the topic of triangles. In this question, we will find the third side of the triangle. In solving this question, for finding the third side of the triangle, we will use the formula of Pythagorean Theorem. The formula for Pythagorean Theorem can be understood by the following:

The formula is: \[{{\left( \text{AB} \right)}^{2}}+{{\left( \text{BC} \right)}^{2}}={{\left( \text{AC} \right)}^{2}}\]

Complete step-by-step answer:
Let us solve this question.
In this question, we have asked to find the missing time of a triangle. The other two sides of a triangle are given as 12mm and 15mm.
As we can see in the question, the question does not say which side is given as hypotenuse, so we will first solve the question by taking hypotenuse as 15mm and the other side as 12mm. After that, we will solve the question by letting the hypotenuse be unknown and the other two sides as given.
So, let us first take hypotenuse as 15mm and the other side as 12mm.
Let the third side be x, then we can write the formula of Pythagorean Theorem as
\[{{\left( x \right)}^{2}}+{{\left( 12 \right)}^{2}}={{\left( 15 \right)}^{2}}\]
The above can also be written as
\[\Rightarrow {{x}^{2}}+144=225\]
\[\Rightarrow {{x}^{2}}=225-144\]
\[\Rightarrow {{x}^{2}}=81\]
Taking square root both side of the equation, we can write
\[\Rightarrow x=\sqrt{81}=9\]
So, we get that the third side is 9mm.
Now, let us solve for the hypotenuse side where other sides are 12mm and 15mm. Let the side of hypotenuse be x. Then, using formula of Pythagorean Theorem as
\[{{\left( 12 \right)}^{2}}+{{\left( 15 \right)}^{2}}={{\left( x \right)}^{2}}\]
The above can also be written as
\[\Rightarrow 144+225={{x}^{2}}\]
\[\Rightarrow 369={{x}^{2}}\]
\[\Rightarrow {{x}^{2}}=369\]
Taking square root to the both side of equation, we can write
\[\Rightarrow x=\sqrt{369}\]
So, we get that the size of the hypotenuse is \[\sqrt{369}\]mm.

Note: We should have a better knowledge in the topic of triangles to solve this type of question easily. We should know the formula of Pythagorean Theorem because they are very helpful in this type of question. And remember that the hypotenuse side is always bigger than the other side of the triangle.