Asquare has an area of 81x square cm. what is the perimeter of the square ?

The perimeter of the square is

Step-by-step explanation:

step 1

Find the length side of the square

we know that

The area of a square is equal to

where

b is the length side of the square

we have

substitute and solve for b

square root both sides

step 2

Find the perimeter of the square

we know that

The perimeter of the square is equal to

we have

substitute

Step-by-step explanation:

Let AC = x

AB - AC = 4 cm

AB = 4 +x  ----------------(I)

Pythagorean theorem

AB² + AC² =BC²

(4 + x)² + x² = 9²

Use the identity (a + b)² = a² + 2ab + b² where a = 4 & b = x

4² +2*4*x  +x² + x²= 81

16 + 8x + 2x² = 81

2x² + 8x + 16 - 81 = 0

2x² + 8x - 65= 0

a = 2 ; b = 8 ; c = -65

D = b² - 4ac

   = 8² - 4*2*(-65)

  = 64 +  520

D = 584

√D = √584 = 24.16

  {Ignore this as it is negative.}

x = 16.16/4

x = 4.04

AC = 4.04 Cm

AB = 4 + 4.04 = 8.04 cm

Area of triangle ABC =

                                   = 16.24 sq.cm