The length of the diagonal of the rectangle is 6.4 units long.
Step-by-step explanation:
Step 1:
From the question, we have the length of two sides of the rectangle is 5 units. The points (4, 0) and (4, 4) have the same x coordinates but different y coordinates.
The difference between the y values gives us the length of the other two sides.
So the length of two sides of the rectangle is 5 while the width of the rectangle is 4 units.
Step 2:
With two sides and the diagonal, a right-angled triangle can be formed.
The hypotenuse is the diagonal and assume it is x units long.
The other two sides are 4 and 5 units long.
According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
[tex]x^{2} = 4^{2} + 5^{2} = 41.[/tex]
[tex]x = \sqrt{41} = 6.4031[/tex] units.
The length of the diagonal of the rectangle is 6.4 units long.
