Question

Find NM
--------------------------------

Answer 1

`MN= \boxed{15}`

Explanation:

refer the attachment

therefore Let,

• 
  `a = x - 3 + 16 = x + 13`
• 
  `b = x - 3`
• 
  `c = x + 3`

according to the question

`\displaystyle (x - 3 ) (x + 13) =( x + 3 {)}^(2)`

simplify square and Multiplication:

`\displaystyle {x}^(2) + 10x - 39 = {x}^(2) + 6x + 9`

cancel x² from both sides:

`\displaystyle 10x - 39 = 6x + 9`

cancel 6x from both sides:

`\displaystyle 4x - 39 = 9`

add 39 to both sides:

`\displaystyle 4x = 48`

divide both sides by 4:

`\displaystyle \boxed{x = 12}`

given that,

`MN= x + 3`

substitute the got value of x:

`MN= 12 + 3`

simplify addition hence,

`MN= \boxed{15}`