So I am doing a Math Unit Test! I need help with a few Questions!
1. LMNP is a rectangle. Find the value of x and the length of each diagonal.
LN = 5x + 21 and MP = 9x - 7
x = ?
LN = ?
MP = ?
2. Can you conclude that the parallelogram is a rhombus, a rectangle, or a square? Explain.
Choose the correct answer below.
A. The parallelogram is a rectangle.
B. No determination can be made with the given information,
C. The parallelogram is a rhombus
D. the parallelogram is a square
Choose the correct explanation below.
A. The diagonals of the parallelogram are congruent.
B. The determination can be made with the given information
C. The parallelogram is both a rhombus and a rectangle
D. The diagonal of the parallelogram bisects a pair of opposite angles.
E. The diagonal of the parallelogram are perpendicular!
3. For what value of x is the given parallelogram a rhombus?
(2x+47) and (8x-7)
The given parallelogram is a rhombus when x = ?
This is Geometry MathXL 2.21 Test
For the first question:
1. To find the value of x, we can set the lengths of LN and MP equal to each other since they are opposite sides of a rectangle. So, we have the equation:
5x + 21 = 9x - 7
You can solve this equation by subtracting 5x from both sides and adding 7 to both sides:
21 + 7 = 9x - 5x
28 = 4x
Now, divide both sides by 4 to solve for x:
x = 7
2. To find the lengths of LN and MP, substitute x = 7 into the given expressions:
LN = 5(7) + 21 = 35 + 21 = 56
MP = 9(7) - 7 = 63 - 7 = 56
Therefore, the value of x is 7, the length of LN is 56, and the length of MP is 56.
For the second question:
To determine if the parallelogram is a rhombus, rectangle, or square, we need more information. The given options do not provide enough information to make a definite conclusion. Therefore, the correct answer is B. No determination can be made with the given information.
For the third question:
To find the value of x for the parallelogram to be a rhombus, we need to set the lengths of the opposite sides equal to each other. So, we have the equation:
2x + 47 = 8x - 7
To solve this equation, subtract 2x from both sides and add 7 to both sides:
47 + 7 = 8x - 2x
54 = 6x
Now, divide both sides by 6 to solve for x:
x = 9
Therefore, the given parallelogram is a rhombus when x = 9.