Question

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

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.
$$3x+1 - 3x=6x - 5-3x$$
$$1 = 3x-5$$
Then 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 $MP$).
$LN=3x + 1=3\times2+1=6 + 1=7$
$MP=6x - 5=6\times2-5=12 - 5=7$

Answer:

$x = 2$, length of each diagonal is 7