Question

What is the length of a diagonal of a rectangle with length 12 and width 5?

Answer 1

Hint: For solving this question you should know about the rectangle and its properties. A rectangle is a quadrilateral which contains all right angles and the width of a rectangle cannot be equal to the length because if these will be equal then it will be square. So, both sides are different but opposite sides of a rectangle are equal to each other.

Complete step by step solution:
According to the question we have to calculate the diagonal of a rectangle whose sides are given as length 12 and width is 5.
Now, if we make a diagram of a rectangle than we will see the elements in that:

According to this diagram of a rectangle we can say that the length of this is equal to y and width is x and the diagonal is z.
As we know, the Pythagoras theorem states that the square of a diagonal in any triangle is equal to the sum of square of width and square of length.
So, here we can write it as: \[{{z}^{2}}={{x}^{2}}+{{y}^{2}}\]
And the diagonal will be \[z=\sqrt{{{x}^{2}}+{{y}^{2}}}\]
If we look out our question and make the diagram for this then it will be like:

So, if we calculate the diagonal z in this diagram then we have to consider ABC as a triangle.
So, the diagonal of \[\vartriangle ABC\] is:
By the Pythagoras theorem \[ {{z}^{2}}={{\left( 5 \right)}^{2}}+{{\left( 12 \right)}^{2}}\]
By solving this \[ {{z}^{2}}=25+144\]
By taking square root both side \[\Rightarrow z=\sqrt{169}=13\] unit
So, the length of the third side of the triangle ABC is 13 units. And this is also the diagonal of this rectangle.

Note: During solving this type of question we should be careful for taking the width and length and for making any triangle in any shape because we can make any triangle in any shape if there is any right angle between the legs which we are taking for the use of width and length. And only there we can apply the Pythagoras theorem.
And if any rectangle is given then we can calculate the diagonal by any one triangle because it will be four triangles there.