Question

if the area of a square is a2 + b2/4 + c2/9 + ab + b2/3 + 2/3ca . find the perimeter of the square​

Answer 1

Answer:

Perimeter of square = 4a + 2b + (4c/3)

Step-by-step explanation:

${\small{\tt{ a^2 + \dfrac{b^2}{4} + \dfrac{c^2}{9} + ab + \dfrac{bc}{3}+ \dfrac{2}{3}ca }}} \\ \\ { \small{ \implies{ \tt{ {(a)}^{2} + { ( \dfrac{b}{2} )}^{2} + { ( \dfrac{c}{3} )}^{2} + 2(a)( \dfrac{b}{2} ) + 2( \dfrac{b}{2} )( \frac{c}{3} ) + 2( \frac{c}{3} )(a)}}}}\\ \\ { \small{ \implies{ \tt{{(a + \frac{b}{2} + \frac{c}{3} )} ^{2} }}}} \\ \\ { \small{ \implies{ \tt{(a + \frac{b}{2} + \frac{c}{3} )(a + \frac{b}{2} + \frac{c}{3} )}}}}$

Therefore, possible side of square is a +b/2 + c/3

Now, find the perimeter of square by using the formula 4 × side

PERIMETER OF SQUARE = 4(a+b/2+c/3)

→ Perimeter of square = 4( {6a + 3b + 2c}/6)

→ Perimeter of square = 2( {6a + 3b + 2c }/3

→ Perimeter of square = 2 ( 2a + b + {2c/3} )

→ Perimeter of square = 4a + 2b + (4c/3)