Question

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

Explanation:

Step1: Recall 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:
$3x+1 - 3x=6x - 5-3x$
$1 = 3x-5$
Add 5 to both sides:
$1 + 5=3x-5 + 5$
$6 = 3x$
Divide both sides by 3:
$\frac{6}{3}=\frac{3x}{3}$
$x = 2$

Step3: Find the length of the diagonals

Substitute $x = 2$ into the expression for $LN$ (we could also use the expression for $MP$).
$LN=3x + 1=3\times2+1=6 + 1=7$
Since $LN = MP$, $MP = 7$ too.

Answer:

$x = 2$, length of $LN=7$, length of $MP = 7$