Question

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

Answer 1

Answer:

$MN= \boxed{15}$

Step-by-step 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,

$MN= \boxed{15}$