All ACT Math Resources
Example Question #1 : How To Find The Length Of The Side Of A Square
If the area of the square is 100 square units, what is, in units, the length of one side of the square?
Example Question #2 : How To Find The Length Of The Side Of A Square
In Square , . Evaluate in terms of .
If diagonal of Square is constructed, then is a 45-45-90 triangle with hypotenuse . By the 45-45-90 Theorem, the sidelength can be calculated as follows:
Example Question #3 : How To Find The Length Of The Side Of A Square
The circle that circumscribes Square has circumference 20. To the nearest tenth, evaluate .
The diameter of a circle with circumference 20 is
The diameter of a circle that circumscribes a square is equal to the length of the diagonals of the square.
If diagonal of Square is constructed, then is a 45-45-90 triangle with hypotenuse approximately 6.3662. By the 45-45-90 Theorem, divide this by to get the sidelength of the square:
Example Question #413 : Act Math
Rectangle has area 90% of that of Square , and is 80% of . What percent of is ?
The area of Square is the square of sidelength , or .
The area of Rectangle is . Rectangle has area 90% of that of Square , which is ; is 80% of , so . We can set up the following equation:
As a percent, of is
Example Question #4 : How To Find The Length Of The Side Of A Square
Reducing the area of a square by 12% has the effect of reducing its sidelength by what percent (hearest whole percent)?
The area of the square was originally
being the sidelength.
Reducing the area by 12% means that the new area is 88% of the original area, or ; the square root of this is the new sidelength, so
Each side of the new square will measure 94% of the length of the old measure - a reduction by 6%.
Example Question #5 : How To Find The Length Of The Side Of A Square
The circle inscribed inside Square has circumference 16. To the nearest tenth, evaluate .
The diameter of a circle that is inscribed inside a square is equal to its sidelength , so all we need to do is find the diameter of the circle - which is circumference 16 divided by :
Example Question #6 : How To Find The Length Of The Side Of A Square
Refer to the above figure, which shows equilateral triangle inside Square . Also, .
Quadrilateral has area 100. Which of these choices comes closest to ?
Let , the sidelength shared by the square and the equilateral triangle.
The area of is
The area of Square is .
By symmetry, bisects the portion of the square not in the triangle, so the area of Quadrilateral is half the difference of those of the square and the triangle. Since the area of Quadrilateral is 100, we can set up an equation:
Of the five choices, 20 comes closest.
Example Question #7 : How To Find The Length Of The Side Of A Square
Find the length of the side of a square given its area is .
To find side length, simply take the square root of the volume. Thus,