Question

lmnp is a rectangle. find the value of x and the length of each diagonal. ln = 3x + 1 and mp = 6x - 5
x = 2
ln =

Explanation:

Step1: Use rectangle property

In a rectangle, the diagonals are equal. So $LN = MP$.
$3x + 1=6x - 5$

Step2: Solve for x

Subtract $3x$ from both sides:
$1 = 6x-3x - 5$
$1=3x - 5$
Add 5 to both sides:
$1 + 5=3x$
$6 = 3x$
Divide both sides by 3:
$x=\frac{6}{3}=2$

Step3: Find the length of LN

Substitute $x = 2$ into the expression for $LN$.
$LN=3x + 1=3\times2+1$
$LN=6 + 1=7$

Answer:

$LN = 7$