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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

User Sally CJ
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2 Answers

5 votes
Pythagoras tells us that the diagonal is √(9²+40²) = 41.
Answer C.
User LarsTech
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3 votes

Answer:

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

A rectangle has a width of 9 units and a length of 40 units. What is the length of-example-1
User SiberianGuy
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