Question

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

Answer 1

Answer:

Length of a diagonal = 41 units

Step-by-step 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, $(AC)^{2}=(40 )^{2} + (9)^{2}$

$(AC)^{2}=1681$

$AC=\sqrt{1681}$

$AC=41$

Hence, Length of a diagonal = 41 units

Answer 2

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