Quadrilateral QRST is a square. If the measure of QR is 3x – 6 and TS is 6 - x. Find the area of the square.
area = (3x-6)(6-x)
= .....
To find the area of the square, we need to know the length of one side since all sides of a square are equal.
Given that QRST is a square, we know that QR = QS = ST = TR.
Let's equate the expressions for QR and TS:
3x - 6 = 6 - x
Next, let's solve for x.
Adding x to both sides, we have:
3x + x - 6 = 6
Combining like terms, we have:
4x - 6 = 6
Adding 6 to both sides, we have:
4x = 12
Dividing both sides by 4, we have:
x = 3
Now that we know x = 3, we can substitute this value back into the expressions for QR and TS.
QR = 3x - 6 = 3(3) - 6 = 9 - 6 = 3
TS = 6 - x = 6 - 3 = 3
Since all sides of the square are equal, we can conclude that the length of one side is 3.
To find the area of the square, we square the length of one side:
Area = side^2 = 3^2 = 9
Therefore, the area of the square is 9 square units.
To find the area of the square, we first need to find the length of one side of the square.
Given that QRST is a square, we know that all four sides are equal. Therefore, we can set the two expressions for the sides equal to each other:
3x - 6 = 6 - x
Now, let's solve this equation to find the value of x:
3x + x = 6 + 6
4x = 12
x = 12/4
x = 3
Now that we have the value of x, we can substitute it back into one of the expressions to find the length of one side of the square:
QR = 3x - 6 = 3(3) - 6 = 9 - 6 = 3
The length of one side of the square is 3.
To find the area of the square, we square the length of one side:
Area = side * side = 3 * 3 = 9.
Therefore, the area of the square is 9 square units.
note that since we have a square,
3x-6 = 6-x
x = 3
side = 3
area = 32 =9