Question

true or false :When the side of a square is decreased in length by 1 foot, its area is 8 ft2. The length of a side of the square is (equation below)

Answer 1

13

Answer 2

the length of a side of a square is \[1+2\sqrt{2}\]

Answer 3

so what's the question then?

Answer 4

sorry, i didnt finish it, it's a true or false question

Answer 5

oh lol

Answer 6

(1+2sqrt(2)-1)^2 ?= 8

Answer 7

(2sqrt(2))^2 = 2^2sqrt(2)^2 = ?

Answer 8

when the side of a square is decreased in length by 1 then the area is 8

so (x-1)^2 = 8

expand the binomial

x^2 - 2x + 1 = 8

now subtract 8 from both sides

x^2 - 2x + 1 - 8 = 8 - 8

combine like terms

x^2 - 2x - 7 = 0

use quadratic formula
\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]
substitute the values
\[x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(-7)}}{2(1)}\]
do you think that equals \(1 +2\sqrt 2\)?

Answer 9

it gave you the size of the square ^^^ this is way to much work
for an area of a square to equal 8 we need x^2 = 8
we are told x = (1-2swrt(2) - 1) = x
so find x^2

Answer 10

i'm really confused, can you try to explain step by step?

Answer 11

(1+2sqrt(2)-1)^2 = (2sqrt(2))^2 = 2^2*sqrt(2)^2 = 4*2 = 8

Answer 12

please, is it true or false?

Answer 13

what is the area of a square?

Answer 14

dont the square roots and the squares cancel eachother?

Answer 15

yes hence sqrt(2)^2 = 2

Answer 16

8

Answer 17

how do you find the area of the square with side x?

Answer 18

x^2

Answer 19

what is x here?

Answer 20

1+2squareroot2?

Answer 21

but they said minus one from that so now what is it?

Answer 22

@willow ?

Answer 23

2sqrrt2

Answer 24

so its true?

Answer 25

yes

Answer 26

thanks