Question

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

LN= 4x + 3 and MP = 8x -9

X=

Answer 1

Diagonals are equal

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

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

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

`\\ \rm\Rrightarrow x=3`

Answer 2

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`
• =>
  `(12)/(4) = (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`