Frickin math ticks me off. Help?

Question

Well I didn't learn this concept yet but here it goes. THe question is:

THe bottom of a box is a rectangle with length 5 cm more than the width. The height of the box is 4 cm and its colume is 264 cm cubed. Find the dimensions of the bottom of the box.

This question really ticks me off. I know the answer is 6 and 11 but how! Plz tell me how you guys solved it. Thanks

Answer 1

the volume of a box is L*W*H
where L=length,W= width,H= height.

You are given:
H=4
and you also have:
L=5+W since length is five more than height.

So volume V =264 = L*W*H

plug in what you know about L, W, and H

264 =(5+W)*W*4
Simplify, and you have a quadratic equation to solve, so put it in standard form:
4*W^2 + 20*W - 264 = 0

Now use the quadratic formula to solve for W

W= (-20 +/- sqrt(20^2 - 4*4*(-264))/2*4

W=(-20 +/- 68)/ 8

But a negative value for length doesn't make sense physically, so use the positive root

W=(-20 +68)/8 =48/8 = 6
recall L= W+5 = 11

Answer 2

THe bottom of a box is a rectangle with length 5 cm more than the width. The height of the box is 4 cm and its colume is 264 cm cubed. Find the dimensions of the bottom of the box.

Define W as width
so length = W + 5

W x (W + 5) x 4 = 264

W x (W + 5) = 264/4

W x (W + 5 ) = 66

W2 + 5W = 66

W2 + 5W - 66 = 0

(W - 6)(W +11) =0
therefore W = 6 or W = -11

Since W can't be -11, so W has to be 6cm
so

length = 11cm
width = 6cm
Height = 4cm

p.s. W2 = w squared

Answer 3

When dealing with algebraic problems, first ask yourself; what is everything being compared to? One indicator of what this standard of comparison is, is the width of the rectangle, since the lenght is given to be 5 cm more than the width. This is what we assign our variable, x.

Let x = width of rectangle.
By the problem itself,
x + 5 = length {since the length is 5 cm more than the width}.

Now, what is the formula for the volume of a rectanglar box? The answer to that is

V = (length) x (width) x (height)

We know that the length is (x + 5) and the width is x. We also know that the height is 4, and its volume is 264.

Substitute (x + 5) for length, x for width, 4 for height, and 264 for volume.

264 = (x + 5) (x) (4)

Now, solve this. Expand the right hand side.

264 = 4x(x + 5)

264 = 4x^2 + 20x

Move the 264 to the right hand side

0 = 4x^2 + 20x - 264

Let's divide both sides of the equation by 4, to simplify things.

0 = x^2 + 5x - 66

Now, factor as normal.

0 = (x - 6) (x + 11)

This yields the solutions x = {6, -11}

However, since x is our width, we can never have a negative width. Immediately discard x = -11 as a result, which means

x = 6.

What does that make our length? Recall that it's x + 5. But this time we KNOW x; it's 6! So x + 5 = 6 + 5 = 11. Our length is 11

Therefore, the dimensions of the bottom of the box are 6 cm by 11 cm.

Answer 4

Let W = width of box.
Then length, L = W + 5

Volume = width * length * height

Therefore, 264 = W(W + 5)(4)

DIvide both sides by 4 :
66 = W(W + 5)
= W^2 + 5W

So, W^2 + 5W - 66 = 0

Factorise : (W - 6)(W + 11) = 0

Equating each term to 0 gives W = 6 or W = -11.
But W can't be negative, so W = 6.

If W = 6, then L = 6 + 5 = 11
Thus, length = 11 cm and width = 6 cm.

Answer 5

Let the width of the base = x

Volume = width * length * height

264 = x * (x+5) * 4

Divide by 4

66 = x (x+5)

x^2 +5x = 66 (quadratic equation)

x^2 -5x -66 = 0

(x-6) (x+11) = 0

So the width of the base (x) is either 6 or -11. Last time I checked it was not possible for a box to have side length -11 :-)

Hence the width is 6cm and the length is 6+5 = 11cm

Hope this helps.

Answer 6

x - length of the bottom rectangle in cm
y - width of the bottom rectangle in cm

You have to know how to calculate the volume of the box. It is the area of the bottom rectangle multiplied by the height of the box. The area of the rectangle is x*y:

x = y + 4 - from the condition of the problem
x*y*4 = 264 - the formula for the volume

x = y + 4
x*y = 66 - divide by 4

y*(y + 5) = 66 - substitute for x
y^2 + 5*y - 66 = 0 - quadratic equation
(y + 11)*(y - 6) = 0 - factor

y1 = -11 < 0 (not a solution!)
y2 = 6 > 0 (solution!)

y = 6 => x = 6+5=11

Answer 7

Volume of a box or rectangular prism is just length times width times height.

If you let x represent the width of the box in cm then the length is x + 5 cm.

Sub into the formula and you get
264 = x(x+5)(4)
66 = x^2 + 5x (divided by 4 to make numbers smaller to work with).

x^2 + 5x - 66 = 0 solve this using factoring
(x+ 11)(x-6) = 0
x = -11 is inadmissible as x is alength and must be positive
or
x = 6
if x = 6, x + 5 = 11

There is your answer!

Answer 8

vol=264
vol=width x length x height
length=width +5
so 264= w x (w+5) x4
264/4= w(w+5)
66= w^2 +5w
w^2 +5w -66=0
(w-6)(w+11)=0
gives 6 & -11
so length =11 & width= 6

Answer 9

now volume of a cuboid=length*breadth*height
(let breadth=x)
=> 264 = (x+5)*x*4
=> 264/4 = x^2+5x
=> 66= x^2+5x
=> x^2+5x-66 = 0
=> (x+11)(x-6)=0
=> x+11=0 or x-6=0
=> x= -11 or x=6
but lenght cannot be negative.
Thus breadth is 6 and length is 11

Answer 10

Let the w=x
Therefore l=x+5
depth given=4
so vol ={x(x+5)} x 4=264
divide both sides by 4
then x[x+5]=66 So x = 6