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 = 7
mp =

Explanation:

Step1: Use property of rectangle diagonals

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

Step2: Solve for x

Subtract $3x$ from both sides:
$1 = 3x-5$.
Add 5 to both sides:
$6 = 3x$.
Divide both sides by 3:
$x = 2$

Step3: Find length of MP

Substitute $x = 2$ into the expression for $MP$.
$MP=6x - 5=6\times2 - 5=12 - 5 = 7$

Answer:

$x = 2$
$LN = 7$
$MP = 7$