Question

the area of a rectangle is 54 cm^2. The side lengths are 2x +1 and x+2. What is the measure of each side?

Answer 1

Area of rectangle in terms of side is ?

Answer 2

A=bh so 54+ (2x+1) (x+2) i got that much,,

Answer 3

54=(2x+1) (x+2)
now foil
(2x+1) (x+2)

Answer 4

2x^2 +4x +x +2 =54

Answer 5

then 2x^2 +5x +2 +54

Answer 6

2x^2 +5x -52 =0

Answer 7

is that right??

Answer 8

that is as far as i can get

Answer 9

yes, that is correct.
now tell me factors of 52

Answer 10

not 52,of 52*2 = 104

Answer 11

2x2 x 13

Answer 12

ok, so of 104 it will be 2x2x2 x 13 = 8x13
now can u factorize ?
write 5x as 13x-8x

Answer 13

i don't get this part

Answer 14

2x^2 +5x -52 =0
2x^2 +8x -3x -52 = 0
we basically need 2 numbers whose product is -52x2 =-104 and sum is 5.
so we need to factor 104 as 8x13
so we get those 2 numbers as 8 and -3 (sum=5)
so we write 5x = 8x-3x
now u understand ?

Answer 15

i have to think about that

Answer 16

sorry there is a typo, 104 = 8x13
so we write
5x as 13x-8x (and not 3x)

Answer 17

2 numbers are -8 and 13
product =-104 , sum =5

Answer 18

so x =4

Answer 19

this stuff is way beyond my understanding

Answer 20

yes, x=4 is correct.
the 2 values of x u get is 4,-13/2
but measure of side cannot be negative.
so x is only 4
now put x=4 in 2x+1 and x+2 to get the sides

Answer 21

9cm and 6cm,, that part is easy

Answer 22

i guess i don't understand the factoring

Answer 23

let me show you steps:
2x^2 +5x -52 =0
2x^2 -8x+13x -52 = 0
2x(x-4) +13 (x-4) = 0
(2x+13) (x-4 ) = 0
2x+13 = 0 OR x-4 =0
x= 13/2 OR x=4
when we have ax^2+bx+c=0
we find 2 numbers whose product is c*a and sum is b

Answer 24

ok i'll study this,,,,
tyty!

Answer 25

welcome ^_^
do you want a simple example which you can try to factor ?

Answer 26

yes please

Answer 27

x^2 + 12x + 20 = 0

Answer 28

2 numbers, product 20 , sum 12 ..... ?

Answer 29

oh bother

Answer 30

factor 20

Answer 31

ohhh wait

Answer 32

2x2x5

Answer 33

so now can u find 2 numbers with sum = 12
using 2x2x5 = 20

Answer 34

2 and 10????

Answer 35

that is correct! good :)
so write 12 x as 10x+2x
can u continue now ?
x^2 +10 x+ 2x +20 = 0

Answer 36

i think so

Answer 37

so tell me both factors?

Answer 38

20 and 10

Answer 39

i meant factors of x^2 + 12x + 20

Answer 40

or could you work out values of x in x^2 + 12x + 20 =0

Answer 41

x^2 (10x) (2x) +20 +0

Answer 42

(x*X) (10x) (2x) +20 +0

Answer 43

write it properly as
x*x+ 10x +2x +20 = 0
now factor out x from first 2 terms and 2 from other 2 terms, what u get ?

Answer 44

14x+20+0

Answer 45

how u got 14 ??

Answer 46

x*x is not 2x

Answer 47

i added the x's

Answer 48

12x +20=0

Answer 49

x*x+ 10x +2x +20 = 0
x(x+10) + 2 (x+10) = 0
did u understand this step ?

Answer 50

yes, i think so

Answer 51

next step :
(x+10)(x+2) =0
this ?

Answer 52

yip,, that one i get

Answer 53

next step :
x+10 =0 OR x+2 = 0

Answer 54

don't know

Answer 55

when (x+a)(x+b) =0
then either of x+a or x+b has to be 0 , so that their product is 0
hence x+10 =0 OR x+2 = 0
ok?

Answer 56

ok

Answer 57

that makes sense

Answer 58

now can u find 2 values of x from x+10 =0 OR x+2 = 0
?

Answer 59

yes