Question

How do you find the measure of the diagonal of a rectangle with sides \[20\] and \[48\]?

Answer 1

Hint: In the given question, we have been given that there is a figure. We have been given the measures of its sides. We have to calculate the measure of its diagonal. We are going to solve it by drawing a rectangle, marking points on it, making a diagonal and then applying Pythagoras Theorem on it.

Complete step by step answer:
We are going to use Pythagoras Theorem, which is,
\[{\left( {Hypo} \right)^2} = {\left( {Base} \right)^2} + {\left( {Perp} \right)^2}\]

Consider the given rectangle.
We have to calculate the length of \[AD\].
Consider the right triangle \[\Delta ACD\].
In the given triangle, we are going to use Pythagoras Theorem, which is,
\[{\left( {Hypo} \right)^2} = {\left( {Base} \right)^2} + {\left( {Perp} \right)^2}\]
In this triangle, \[Base = CD = 48\] and \[Perp = AC = 20\].
So, we have,
\[Hypo = AD = \sqrt {A{C^2} + C{D^2}} = \sqrt {{{20}^2} + {{48}^2}} = \sqrt {2704} \]
We know, \[{52^2} = 2704\]
Hence, \[AD = 52\]

Thus, the length of the diagonal is \[52\].

Note: In the given question, we had to find the diagonal of a given rectangle whose sides were given. We did that by using the Pythagoras Theorem. The point where there could be an error is to recognize the perpendicular, base and hypotenuse to calculate one of the unknown quantities. The squares of the perpendicular and base are added, so the side to give care to is hypotenuse – hypotenuse is the side opposite to the right-angle. So, while solving the questions of this type, it is important to remember these points.