ACT Math : How to find the length of the side of a quadrilateral

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : How To Find The Length Of The Side Of A Quadrilateral

Find the length of a rectangle if the area is , and the width is .

Possible Answers:

Correct answer:

Explanation:

Write the formula to solve the area of a rectangle.

Substitute the dimension and area to solve for the length.

Example Question #2 : How To Find The Length Of The Side Of A Quadrilateral

If the perimeter of a square is  and the area is , what is the side length of the square?

Possible Answers:

Correct answer:

Explanation:

The square has 4 equal sides.  Let's assume a side is .

Each side of the square has a length of .

The area of the square is:

Substitute  into the area to solve for .

Since one side of the square is , substitute the value of   to determine the length of the square side.

Example Question #3 : How To Find The Length Of The Side Of A Quadrilateral

Find the side of a square if the area is .

Possible Answers:

Correct answer:

Explanation:

The area of a square is:

Substitute the area and solve for the side.

The quantity inside the square root may not be factorized in attempt to eliminate the square root!

The side length of the square is:

Example Question #4 : How To Find The Length Of The Side Of A Quadrilateral

Q9

Find the perimeter of the rhombus above. 

Possible Answers:

Correct answer:

Explanation:

By definition, a rhombus is a quadrilateral with four equal sides whose angles do not all equal 90 degrees. To find the perimeter, we must find the values of x and y. In order to do so, we must set up a system of equations where we set two sides equal to each other. Any two sides can be used to create these systems.

Here is one example:

Eq. 1

Eq. 2

 

Now we plug  into the first equation to find the value of :

Plugging these values into any of the three equations will give us the length of one side equaling 11.

Since there are four sides, .

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