A rectangle has a width of 9 units and a length of 40 units. What is the length of a diagonal?

Solution: 

Using Pythagoras Theorem, “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.

Also, the Pythagorean equation relates the sides of a right triangle as, if the lengths of any two sides are known the length of the third side can be found.

As shown in the figure, the diagonal ‘d’ denotes the length of the hypotenuse and width of the rectangle ‘w’ and length ‘l’ denotes the lengths of the other two sides.

The Pythagorean theorem can be written as:

l²+ w² = d²

where l is length, w is width and d is diagonal or hypotenuse

Therefore, 40² + 9² =d²

1600 + 81 = d²

⇒ d = √1681

⇒ d = 41 units

A rectangle has a width of 9 units and a length of 40 units. What is the length of a diagonal?

Summary:

For the rectangle having a width of 9 units and a length of 40 units, the length of the diagonal is 41 units.