Question

LMNP is a rectangle. Find the value of x and the length of each diagonal.

Answer 1

Solution:

We know that:

• Given diagonals: LN and MP
• LN and MP must be equal because they are diagonals of LMNP.
• LN = 4x + 3
• MP = 8x - 9

Since LN and MP must be equation, equation formed: 4x + 3 = 8x - 9

Let's simplify the equation to find x.

Subtracting 4x both sides.

• $4x + 3 = 8x - 9$
• => $4x - 4x + 3 = 8x - 9 - 4x$
• => $3 = 4x - 9$

Add 9 both sides.

• => $3 = 4x - 9$
• => $3 + 9 = 4x - 9 + 9$
• => $12 = 4x$

Divide 4 both sides.

• => $12 = 4x$
• => $\frac{12}{4} = \frac{4x}{4}$
• => $x = 3$

Now, let's find the length of each diagonal.

• $LN = 4x + 3 = 4(3) + 3 = 12 + 3 = 15 \space\ units$
• $MP = 8x - 9 = 8(3) - 9 = 24 - 9 = 15 \space\ units$

Answer 2

Diagonals are equal

$\\ \rm\Rrightarrow 4x+3=8x-9$

$\\ \rm\Rrightarrow -4x=-12$

$\\ \rm\Rrightarrow x=-12/-4$

$\\ \rm\Rrightarrow x=3$