Pre - Algebra question. help please?

Question

The area of a rectangle is 120 cm2. the length is 7 cm longer than the width. That are the dimensions of the rectangle. Please help i have been stuck on this for over 1 hour!

Answer 1

okay. start like this. The basic four steps that every freaking teacher stresses.

1) Let x= the width of one side. Let x+7= the length of one side (the lenght is always longer than the width).

2) Now for an equation. Remember that the formula for the area of a rectangle is the "length x width". You already know that the area is 120 cm2. So use your "let statements". (x+7)x=120. this is because you know that your lenght is "x+7" and that your width is "x".

Now simplify:

Distribute. You'll get "x squared" + 7x=120. Now subtract 120 from both sides. This leaves you with "x squared + 7x -120=0. Now you must factor. Now ask yourself this, whenever you encounter factoring problems at the quadratic level (highest exponential power is the second). "What two factors (the numbers that multiply together to give you the product, in this case, is -120) of -120 will add togther to equal 7, the number in the middle?" A possible set of factors would be 15 and -8. They multiply together to equal -120. If you add them together, you'll get 7.

Remember the FOIL method (first, outer, inner, last)

(a+b)(c+d) according to the rule, you'll end up with ac, ad, bc, and bd.

"x squared" + 7x -120 = (x+15)(x-8)=0

earlier, this equation equaled zero, because 120 was subtracted from both sides. Remember, your objective is finding what x is.

(x+15)(x-8)=0
now, for an answer to equal zero here, one or more of the factors (a group in parentheses in this case) must be zero.
x+15=0; x= -15
x-8=0; x= 8

3) (numeric answer) So x= -15 or 8, and x+7= -8 or 15 Now, remember x and x+7 represents width and lenght, respectively. Is there a such thing as negative length in this world? No.

4) (sentence answer) The width of the rectangle is 8 cm, and the lenght of the rectangle is 15 cm.

Answer 2

OK. Start by writing 2 equations:
a = l * w
l = w + 7

Then, plug in numbers and substitutions:
120 cm^2 = (w + 7) * w

Distribute the parenthesis:
120 cm^2 = w^2 + 7w

Subtract 120 from both sides:
0 = w^2 + 7w - 120

Now, use the quadratic equation:
w = (-b +/- (b^2 - 4ac)^1/2)/2a
w = (-7 +/- (49 + 480)^1/2)/2
w = -7/2 +/- 23/2
w = -15 or 8. Ignore the negative answer. (8 is the solution!)
l = w + 7 = 8 + 7 = 15 cm (solution!)

Answer 3

Let x cm be the length of the width hence length of the rectangle will be (x+7)cm.
(x+7)(x)=120
x^(2) +7x-120=0
(x+15)(x-8)=0
x=-15(rejected as xis length so greater than zero) or x=8

Width=8cm
Length=8+7
=15cm

Answer 4

Area = length X width
(A = L X W)
A= 120
L = (w+7)

120 = (w+7) X w
120 = w(w+7)
120 = w2 + 7w
0 = w2 + 7w - 120
0 = (w+15)(w-8)
w = -15, w = 8 <----- the width cannot be negative, so -15 is rejected.

Now:
A= 120
L = (w+7) ----> (8+7) ----> 15
W = 8

check:
120 = 15 X 8 --> correct!

Answer 5

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Answer 6

x = width
x + 7 = length

x(x +7)=120
x2 +7x=120
x2 +7x-120=0
foil method (x+15)(x-8)=0

x=-15 or x=8 8 is width 15 is length

Answer 7

(7+W) x W=120
now solve
7+w=lenght
w= width
solve for w and then substitute whatever u get i for w+7 to get the lenght