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LMNP is a rectangle. Find the value of x and the length of each diagonal. LN=2x+25 and MP=6x−7

User Blacc
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2 Answers

4 votes

Final answer:

The value of x in the rectangle LMNP is calculated by setting the expressions for diagonals LN and MP equal to each other, and solving for x. After finding x = 8, the diagonals' length is determined to be 41 units each, confirming that they are equal, as is true in any rectangle.

Step-by-step explanation:

To find the value of x and the length of each diagonal in rectangle LMNP, we know that diagonals of a rectangle are equal in length. Hence, LN = MP. Setting the expressions for LN and MP equal to each other gives us the equation 2x + 25 = 6x - 7. Solving for x involves the following steps:

  1. Subtract 2x from both sides: 25 = 4x - 7.
  2. Add 7 to both sides: 32 = 4x.
  3. Divide by 4: x = 8.

With the value of x found, we can calculate the length of the diagonals:

  • LN = 2(8) + 25 = 16 + 25 = 41.
  • MP = 6(8) - 7 = 48 - 7 = 41.

This confirms that both diagonals are indeed equal, and their length is 41 units.

User Acelot
by
8.4k points
2 votes
2x+25=6x-7
4x=32
x = 8
LN = 41
MP = 41
User Groodt
by
8.5k points

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