All SAT Math Resources
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?
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 #62 : Quadrilaterals
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?
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 x2 from 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 #633 : Geometry
If the area of a square is 25 inches squared, what is the perimeter?
Not enough information
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 or The perimeter of a square is the sum of the length of all 4 sides or