SAT Math : How to find the length of the side of a square

Study concepts, example questions & explanations for SAT Math

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Example Questions

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

The area of square R is 12 times the area of square T. If the area of square R is 48, what is the length of one side of square T?

 

Possible Answers:

2

4

1

16

Correct answer:

2

Explanation:

We start by dividing the area of square R (48) by 12, to come up with the area of square T, 4.  Then take the square root of the area to get the length of one side, giving us 2.

 

 

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

When the side of a certain square is increased by 2 inches, the area of the resulting square is 64 sq. inches greater than the original square.  What is the length of the side of the original square, in inches?

Possible Answers:

14

17

15

18

16

Correct answer:

15

Explanation:

Let x represent the length of the original square in inches.  Thus the area of the original square is x2.  Two inches are added to x, which is represented by x+2.  The area of the resulting square is (x+2)2.  We are given that the new square is 64 sq. inches greater than the original.  Therefore  we can write the algebraic expression:

x2 + 64 = (x+2)2

FOIL the right side of the equation.

x2 + 64 = x2 + 4x + 4 

Subtract xfrom both sides and then continue with the alegbra.

64 = 4x + 4

64 = 4(x + 1)

16 = x + 1

15 = x

Therefore, the length of the original square is 15 inches.

 

If you plug in the answer choices, you would need to add 2 inches to the value of the answer choice and then take the difference of two squares.  The choice with 15 would be correct because 172 -152 = 64.

 

 

 

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

If the area of a square is 25 inches squared, what is the perimeter?

Possible Answers:

10

20

15

Not enough information

25

Correct answer:

20

Explanation:

The area of a square is equal to length times width or length squared (since length and width are equal on a square). Therefore, the length of one side is l = \sqrt{25in^{2}} or l=5 in. The perimeter of a square is the sum of the length of all 4 sides or 4 \times 5 in. =20 in.

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