If the length of a square is decreased by 1 unit, the area will be 8 square units. Write an equation for the area of the square.

Question

Calculate the original side length as an exact solution. and Calculate the original side length rounded to the nearest hundredth.  

Answer 1

(s-1)^2 = 8 = area of the square when the side is decreased by 1

s^2 -2s +1-8 =0

s^2-2s-7=0

use the quadratic formula

s =-b/2a +sqr(b^2-4ac)/2a

s= 2/2 +(1/2)sqr(2^2 -4(1)(-7))

s= 1 + .5sqr32

s= 1+2sqr2

= about 1+2(1.414)

= about 3.83

s^2 = area of the original square

= (1+2sqr2)^2

= 1+4sqr2+ 8

= 9+4sqr2

= about 9+4(1.414)

= 9+5.656

= about 14.66

Answer 2

(s - 1)² = 8

s² - 2s + 1 = 8

s² - 2s - 9 = 0

Can you use the Quadratic Formula and answer?

Answer 3

Let's call the length of the square x. We know that the area of a square is the its length squared. They indicate that if we increase the length by 1, the area becomes 8. Then, we can write

(x+1)² = 8.

Then,

x+1 = √8 -> x = √8 -1

You can then find what this value is equal to, and round it to the nearest hundredth