# Math Help - Couple of problems. help please

1. ## Couple of problems. help please

hi.
can someone please help with the following:

1. The sides of a cuboid measure 1 cm, a cm and b cm. Its volume is 12cm^3 and its surface area is 38 cm^2.
Find a and b

2. Show that y=x+c is a tangent to x^2 + y^2=4 if, and only if, c^2=8. (Show that if y=x+c is a tangent then c^2=8, and also that if c^2 = 8 then y= x+c is a tangent)

thanks

with the second one ive got as far as
i know the discriminant must equal 0 and the quadratic is 2x^2 +2cx +(c^2-4)=0,
and from the first statment 4c^2-8(c^2-4)=0

2. Originally Posted by sammy28
hi.
can someone please help with the following:

1. The sides of a cuboid measure 1 cm, a cm and b cm. Its volume is 12cm^3 and its surface area is 38 cm^2.
Find a and b

Consider dimensions of the cubiod to be length(L), width(W) and height(H).

lets make (from your information) L = 1, W = a, H = b.

Now solve these equations

1:
$V = L \times W \times H$

$12 = 1 \times a \times b$

$a = \frac{12}{b}$

2:

$SA = 2(L \times W+W \times H+H \times L)$

$38 = 2(1 \times a+a \times b+b \times 1)$

$38 = 2a+2ab+2b$

Now sub the result in 1 into the result in 2

3. thanks pickslides, for some reason i had drawn a net and written the area as:

ab=12
2ab+4b=38

then tried elimination to solve and got wrong answer

if i solve the quadratic in your answer, ie b^2-7b+12=0 then all is well

i need to compare the net with your forumula.

thanks

4. Originally Posted by sammy28
thanks pickslides, for some reason i had drawn a net and written the area as:

ab=12
2ab+4b=38

then tried elimination to solve and got wrong answer

if i solve the quadratic in your answer, ie b^2-7b+12=0 then all is well

i need to compare the net with your forumula.

thanks

$b^2-7b+12=0$

agreed...