Intermediate Geometry : How to find the length of the diagonal of a parallelogram

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #1 : How To Find The Length Of The Diagonal Of A Parallelogram

The length of a parallelogram is  cm and the width is  cm. One of its diagonals measures  cm. Find the length of the other diagonal.  

Possible Answers:

None of the other answers.

 

Correct answer:

 

Explanation:

The formula for the relationship between diagonals and sides of a parallologram is

 ,

where  represents one diagonal, 

 represents the other diagonal, 

 represents a side, and 

 represents the adjoining side.  

So, in this problem, substitute the known values and solve for the missing diagonal. 

So, the missing diagonal is  cm.

Example Question #2 : How To Find The Length Of The Diagonal Of A Parallelogram

Parallogram

In the parallogram above, find the length of the labeled diagonal.

 

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

In a parallogram, diagonals bisect one another, thus you can set the two segments that are labeled in the picture equal to one another, then solve for .  

So, 

.

If , then you can substitute 14 into each labeled segment, to get a total of 52.

Example Question #3 : How To Find The Length Of The Diagonal Of A Parallelogram

In the parallogram below, find the length of the labeled diagonal.

Parallelogram2

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

In a parallelogram, the diagonals bisect one another, so you can set the labeled segments equal to each other and then solve for .  

.  

If , then you substitute 6 into each labeled segment, to get a total of 40.

Example Question #4 : Parallelograms

Para3

In the parallelogram above, find the length of the labeled diagonal.

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

In a parallelogram, the diagonals bisect each other, so you can set the labeled segments equal to one another and then solve for 

.  

Then, substitute 4.8 for  in each labeled segment to get a total of 11.2 for the diagonal length.

Example Question #4 : How To Find The Length Of The Diagonal Of A Parallelogram

Suppose a square has an area of 6.  What is the diagonal of the parallelogram?

Possible Answers:

Correct answer:

Explanation:

Write the formula to find the side of the square given the area.

Find the side.

The diagonal of the square can be solved by using the Pythagorean Theorem.

Substitute and solve for the diagonal, .

Example Question #5 : How To Find The Length Of The Diagonal Of A Parallelogram

If the side length of a square is , what is the diagonal of the square?

Possible Answers:

Correct answer:

Explanation:

Write the diagonal formula for a square.

Substitute the side length and reduce.

Example Question #6 : How To Find The Length Of The Diagonal Of A Parallelogram

Parallelogram  has diagonals  and  and .

True, false, or undetermined: Parallelogram  is a rectangle.

Possible Answers:

False

Undetermined

True

Correct answer:

False

Explanation:

One characteristic of a rectangle is that its diagonals are congruent. Since the diagonals of Parallelogram  are of different lengths, it cannot be a rectangle.

Example Question #8 : Parallelograms

Parallelogram  has diagonals  and  and .

True, false, or undetermined: Parallelogram  is a rhombus.

Possible Answers:

False

Undetermined

True 

Correct answer:

Undetermined

Explanation:

One characteristic of a rhombus is that its diagonals are perpendicular; no restrictions exist as to their lengths. Whether or not the diagonals are perpendicular is not stated, so the figure may or may not be a rhombus.

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