Pergunta

LMNP is a rectangle Find the value of x and the length of each diagonal. LN=5x+20 and MP=8x-4 x= square
Solução

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ValdirMestre · Tutor por 5 anos
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To solve this problem, we need to use the properties of a rectangle and the given information.<br /><br />Given:<br />- LMNP is a rectangle<br />- LN = 5x + 20<br />- MP = 8x - 4<br /><br />In a rectangle, the diagonals are equal in length. Therefore, we can set the lengths of the diagonals equal to each other and solve for x.<br /><br />Step 1: Set the lengths of the diagonals equal to each other.<br />LN = MP<br />5x + 20 = 8x - 4<br /><br />Step 2: Solve for x.<br />5x + 20 = 8x - 4<br />20 + 4 = 8x - 5x<br />24 = 3x<br />x = 8<br /><br />Step 3: Find the length of each diagonal.<br />LN = 5x + 20 = 5(8) + 20 = 40 + 20 = 60<br />MP = 8x - 4 = 8(8) - 4 = 64 - 4 = 60<br /><br />Therefore, the value of x is 8, and the length of each diagonal is 60.
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