Pergunta

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

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MartimMestre · Tutor por 5 anos
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The value of \(x\) is \(8\), the length of \(LN\) is \(60\), and the length of \(MP\) is also \(60\).
Explicação
## Step 1<br />In a rectangle, the diagonals are equal. Therefore, we can set the expressions for the diagonals \(LN\) and \(MP\) equal to each other and solve for \(x\).<br /><br />### \(5x + 20 = 8x - 4\)<br /><br />## Step 2<br />Solving the equation for \(x\), we subtract \(5x\) from both sides to get:<br /><br />### \(20 = 3x - 4\)<br /><br />Then, add \(4\) to both sides to get:<br /><br />### \(24 = 3x\)<br /><br />Finally, divide both sides by \(3\) to solve for \(x\):<br /><br />### \(x = 8\)<br /><br />## Step 3<br />Now that we have the value of \(x\), we can substitute it back into the expressions for \(LN\) and \(MP\) to find their lengths.<br /><br />For \(LN\), we substitute \(x = 8\) into the expression \(5x + 20\):<br /><br />### \(LN = 5(8) + 20 = 40 + 20 = 60\)<br /><br />For \(MP\), we substitute \(x = 8\) into the expression \(8x - 4\):<br /><br />### \(MP = 8(8) - 4 = 64 - 4 = 60\)
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