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Solving for 2 unknowns... Please help with algebra problem! I'm STUCK!?
This might sound pathetic, but I have been stuck on this problem for almost an hour! I can't figure out what I am doing wrong...
The length of a rectangular frame is 3 1/2 inches longer than the width. If the perimeter is 42 inches, what are the dimensions of the frame?
I have a test Monday and I am studying...but can't figure this out! Thanks.
Also,
A piece of steel is welded to a horizontal truss forming two angles with the truss. The larger of the 2 angles is 2 1/2º more than twice the smaller angle. Find the angle measurements.
What are the formula/s for these problems?
Thanks! Now I can go to sleep! I have been studying for over 12 hours just today... not counting the past week!!
8 Answers
- Anonymous1 decade agoFavorite Answer
That's just pathetic.
- 1 decade ago
Let x = width of the frame
x + 3.5 = length of the frame
P = 42 in
use the perimeter formula of a rectangle to get the dimensions of the frame
P = 2L + 2W, and plug the data you know in the equation
42 = 2(x + 3.5) + 2(x)
solve for x by:
1. distributing the 2
42 = 2x + 7 + 2x
2. combine like terms
42 = 4x + 7
3. subtract the 7
35 = 4x
4. divide 35 by 4 to isolate the x
8.75 = x
x = width of the frame = 8.75 inches
x + 3.5 = length of the frame = 8.75 + 3.5 = 12.25 inches
hope this makes sense!
good luck on your test!
Source(s): Chemistry major,....a lot of math classes taken! :) - 1 decade ago
It's just a simple substitution problem.
Start with what you already know, your length(L) is 3.5 in more than your width (W).
L= W+3.5
Starting with the equation for your perimeter, P= 2L+2W, you can substitute 42 for P giving you
42=2L+2W
Substitute your L value (W+3.5) into the equation for the perimter and you get
42= 2(w+3.5) +2 w
Work it out and you get
42= 2w + 7 + 2w
Which equates to
42= 4w + 7
Subtract 7 from 42 giving you
35= 4w
Divide by 4 giving you
35/4=w or 8.75.
Plug 8.75 into your original formula L= w+3.5 giving you
L= 8.75 + 3.5
Giving you a length of 12.25 which is 3.5!
Hopefully this all helps, sorry if I've made any errors in my math, haven't done this in 4 or 5 years.
Source(s): In the time it took me to figure this out, and type it out, 5 people answered . Sorry. - 1 decade ago
L = W + 3.5
Two lengths and two widths make the perimeter of 42 inches. 2L + 2W = 42
But Length = W + 3.5
2(W + 3.5) + 2(W) = 42
2W + 7 + 2W = 42
2W + 2W = 35
So, yeah, just solve for "Width," and then add 3.5 units for the Length. Why don't they use base and height any more? I'm really tired, so i'm not sure if it's gonna work, so just test it to see.
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- Anonymous1 decade ago
There are 4 sides to a rectangle, and the opposite sides are equal.
side 1 = x
side 2 = x+3.5
side 3 = x
side 4 = x+3.5
the perimeter is the sum of all the sides so...
x+x+x+3.5+x+3.5=42
4x+7=42
-7 -7
4x=35
x=35/4
x=8.2in
so...
side 1 = 8.2 in
side 2 = 8.2+3.5 = 11.7
and so on.
- Anonymous1 decade ago
let the width be x inches
and the length is 3.5 inches longer than the width so: length = x+3.5
2 sides of the rectangle = x
2 sides of the rectangle = x+3.5
perimeter =sum of the 4 sides =42
so,
2(x) + 2(x+3.5) = 42
2x + 2x + 7 = 42
4x = 35
x = 35/4
x = 8.75 inches
therefore width = x =8.75 inches
and length = x+3.5 = 12.25 inches
- 1 decade ago
the equation should be 2x + 2(x+3.5)=42 --> 2x+2x+7=42 --> 4x+7=42 then subtract 7 from both sides and solve for x (which should be 8.75) and length = 12.25
- 1 decade ago
L=W+3.5 *Substitute this in the perimeter equation
2(W+L)=42
2(W+(W+3.5))=42
Solve for W
