Question

Is I have a rectangular prism which basis area is 12 cm^2 and height 8 cm, then calculate the values of "a" and "b" where "a" and "b" are basis dimensions... The best medal ever

Answer 1

@pooja195

Answer 2

a rectangular prism has a base of rectangle

area of a rectangle is ??? do you know this formula ?

Answer 3

area= a*b

Answer 4

exactly

so you need getting two integers a and b with product equal 12

Answer 5

ok. one choice may be 12 = 3*4

right ?

Answer 6

look at that image

Answer 7

I need to find Lateral area, total area and volume

Answer 8

this image dont change nothing for you get this a and b

Answer 9

I found volume value which is 96 cm^3

Answer 10

yes sure this was easy bc. V = area of base time height so = 12*8 = 96 cm^3

Answer 11

12= 6*2

12= 4*3

12= 12*1

12= 2sqrt(3)*2sqrt(3)

Answer 12

2sqrt3 not can being bc. this is a rectangle not a square

Answer 13

I already know the answers, but I just wanna know how to get the answer no making assumptions

Answer 14

and so the a need being different the b

Answer 15

do you get me?

Answer 16

that's right! a is different than b

Answer 17

bc. in this text of your exercise given just these details so there are much possibility

how you ve wrote above

3*4
6*2
12*1

Answer 18

Could you find a formula that relates basis area with that basis rectangle perimeter?

Answer 19

why ? do you know the perimeter too ?

Answer 20

area = a*b
perimeter = 2(a+b)

Answer 21

I don't xD... That's why I want to find that formula... I already have the area value

Answer 22

I guess that the only way to solve this exercise is by making assumptions of "a" and "b" values

Answer 23

don't you think?

Answer 24

ok.

a*b = 12 => a = 12/b

P = 2a +2b =2*(12/b) +2b

do you think it so ?

Answer 25

\[perimeter = \frac{ 24 }{ b }+2b\]
\[perimeter = \frac{ 24+2b^2 }{ b }\]
\[b*perimeter=24+2b^2\]
\[2b^2-b*perimeter+24=0\]

\[b=\frac{ perimeter ∓ \sqrt{(-perimeter)^{2}-4*2*24}}{ 4 }\]

Answer 26

I still have an unknow value which is perimeter... @jhonyy9

Answer 27

your statement is incomplete.
dimensions of base may be 1*12,2*6,3*4
if a and b are integers.

a*b=12
p=2(a+b)
=2(1+12)=26
or =2(2+6)=16
or =2(3+4)=14
if a and b are real numbers ,then there are infinite real numbers (a neq 0,b neq 0)
such that ab=96
a=96/b
p=2(a+b)=2((96/b)+b)

Answer 28

in your case b is real
so\[P^2-4*2*24 \geq 0\]
\[P^2 \geq 4*16*3\]
\[\left| P \right|\geq 8\sqrt{3}\]
so \[P \leq-8\sqrt{3}~or P \geq 8\sqrt{3}\]
perimeter can not be negative
Hence \[P \geq 8\sqrt{3}\]
so minimum value of perimeter is\[8\sqrt{3}\]

Answer 29

thanks a lot @sshayer :)

Answer 30

correction write 12 in place of 96

Answer 31

yw