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LMNP is a rectangle.Find the value of x and the length of each diagonal. LN=x and MP=4x-21 x=7 (Simplify your answer.) LN=7 (Simplify your answer.) MP=square (Simplify your answer.)

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LMNP is a rectangle.Find the value of x and the length of each diagonal.
LN=x and MP=4x-21
x=7 (Simplify your answer.)
LN=7 (Simplify your answer.)
MP=square  (Simplify your answer.)

LMNP is a rectangle.Find the value of x and the length of each diagonal. LN=x and MP=4x-21 x=7 (Simplify your answer.) LN=7 (Simplify your answer.) MP=square (Simplify your answer.)

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JoãoMestre · Tutor por 5 anos

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To find the value of x and the length of each diagonal in the rectangle LMNP, we can use the properties of a rectangle.<br /><br />In a rectangle, the diagonals are congruent, meaning they have the same length. Therefore, we can set up the equation:<br /><br />LN = MP<br /><br />Given that LN = x and MP = 4x - 21, we can substitute these values into the equation:<br /><br />x = 4x - 21<br /><br />Now, let's solve for x:<br /><br />x - 4x = -21<br />-3x = -21<br />x = 7<br /><br />So, the value of x is 7.<br /><br />Now, let's find the length of each diagonal:<br /><br />LN = x = 7<br />MP = 4x - 21 = 4(7) - 21 = 28 - 21 = 7<br /><br />Therefore, the length of each diagonal is 7.
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