Question

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

A. 31 units
B. 39 units
C. 41 units
D. 49 units

Answer 1

Pythagoras tells us that the diagonal is √(9²+40²) = 41.
Answer C.

Answer 2

Length of a diagonal = 41 units

Explanation:

Given : A rectangle has a width of 9 units and a length of 40 units.

To Find : the length of a diagonal

Solution :

Since all angles of rectangle measures 90°.

So, to find length of diagonal use Pythagoras theorem i.e.

`(Hypotenuse)^(2)=(Perpendicular )^(2)  + (Base)^(2)`

Refer attached figure

Since ΔADC is right angled triangle

So,
`(AC)^(2)=(AD )^(2)  + (DC)^(2)`

Where AC is the diagonal

AD = Length = 40 units

DC= Width = 9 units

Thus,
`(AC)^(2)=(40 )^(2)  + (9)^(2)`

`(AC)^(2)=1681`

`AC=√(1681)`

`AC=41`

Hence, Length of a diagonal = 41 units