Answer:
Therefore the diagonal is 31.6 unit.
Step-by-step explanation:
Given:
In a Rectangle
Length = L = 30 unit = Longer Leg
Width = W = 10 unit = Shorter Leg
Diagonal = d = Hypotenuse
To Find:
Relation between L ,W and d
d = ?
Solution:
In a Rectangle vertex angles are 90°
In Right Angle Triangle , By Pythagoras theorem we have
[tex](\textrm{Hypotenuse})^{2} = (\textrm{Longer leg})^{2}+(\textrm{Shorter leg})^{2}[/tex]
Substituting the values we get
[tex](d)^{2} = (L)^{2}+(W)^{2}[/tex]
i.e [tex]L^{2}+W^{2}=d^{2}[/tex] .........Relation between L ,W and d
Now Substituting L = 30 ,W =10 we get
[tex](d)^{2} = (30)^{2}+(10)^{2}\\d^{2}=1000\\Square\ Rooting\\d=\pm \sqrt{1000}\\d=31.6\ unit\ as\ d\ cannot\ be\ negative[/tex]
Therefore the diagonal is 31.6 unit.
