Given:
Shape of the shelf is a right triangle.
Width of the shelf = 9 inches
Length of the shelf = 40 inches
He believes the diagonal will be 41 inches.
To find:
Whether he is accurate or not.
Solution:
According to the Pythagoras theorem,
[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]
Using Pythagoras theorem, find the length of the diagonal.
[tex]Diagonal^2=Width^2+length^2[/tex]
[tex]Diagonal^2=(9)^2+(40)^2[/tex]
[tex]Diagonal^2=81+1600[/tex]
[tex]Diagonal^2=1681[/tex]
Taking square root on both sides.
[tex]Diagonal=\pm \sqrt{1681}[/tex]
But side cannot be negative.
[tex]Diagonal=41[/tex]
Therefore, the length of the diagonal is 41 inches. So, John is accurate.
