Answer:
The length of the diagonal = 22.20 cm
Step-by-step explanation:
Here, the length of the rectangle = 18 cm
Also, the width of the rectangle = 13 cm
Let us assume the diagonal of the rectangle = k cm
As we know, EACH INTERIOR ANGLE OF THE RECTANGLE = 90°
So, if we join the opposite vertices of the rectangle, a Right angled triangle is formed.
Here, the length of the Rectangle = Perpendicular of the right Δ
Width of the Rectangle = Base of the right Δ
Diagonal of the Rectangle = Hypotenuse of the right Δ
Now, by PYTHAGORAS THEOREM:
[tex](Base)^2 + (Perpendicular)^2 = ( Hypotenuse)^2[/tex]
or, [tex](Width)^2 + (Length)^2 = ( Diagonal)^2[/tex]
[tex]\implies (13)^2 + (18)^2 = (m)^2\\\implies 169 + 324= m^2\\\implies m^2 = 493\\\implies m = \sqrt{493} = 22.20[/tex]
or, Diagonal = 22.20 cm
Hence, the length of the diagonal = 22.20 cm
