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 Posted: Thu Feb 04, 2010 2:26 pm
The length of a rectangle is 7 cm longer than the width. The perimeter is 38 cm.Find the length and width of the rectangle.
Length = cm
Width = cm
The teacher hasn't even taught this to us yet and its on my HW. How do I approach this?
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Posted: Fri Feb 05, 2010 10:05 pm
ok 1st remember how you calculate the perimeter of the rectangle. To calculate any perimeter you just add up the length of the sides.
for a rectangle the sides are the width (call it w) and the height (call it h)
so the perimeter= w + w + h + h
or p= 2*w+2*h
so lets set it up.
38 = 2*w+2*7
38 = 2*w + 14
solve it algebraically by subtracting both sides by 14
24 = 2*w
divide both sides by 2
12 = w
so the width is 12, and the height (which was given to us) was 7
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Posted: Fri Feb 05, 2010 11:46 pm
O.o
but if its 7 more than the width can't it be 7 more than any #? I'm kinda lost.
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Posted: Sun Feb 07, 2010 12:18 am
opps that's what I get for not reading the directions >>, sorry let's try this again...
The length of a rectangle is 7 cm longer than the width. The perimeter is 38 cm.Find the length and width of the rectangle.
The perimeter is still calculated the same way
p=2w+2L
38=2w+2L
but we're not given the length, ninja . So currently we can't solve this because we have 2 unknowns, and only 1 equation. In order to solve for 2 unknowns we need 2 equations, lets see if the teacher gave us any more information...
We do know the length is 7 more cm then the width, so lets set up an equation using that.
L=w+7
this is the equation that literally shows us the the length is ('is' is our equal sign) 7 more than ("more than" is our plus sign) the width.
Now we have 2 equations and 2 unknowns, now we can solve
using our equation
L=w+7
Let's plug in w+7 for the L's in the other equation
38=2w+2*(L)
we know that L is equal to w+7 so we can change it
38=2w+2*(w+7)
lets do the math now
38=2w+2w+14
38=4w+14
solve this with algebra... subtract both sides by 14
24=4w
divide by 4
6=w
ok now to find the length we just remember that its 7 more than the width, or just plug w back into that equation
L=w+7
L=6+7
L=13
we can check our answer too
Just figure out what 2*L+2*w is given our new numbers... hopefully the answer is 38
2*13+2*6
26+12=38 so yay! we did it right!
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Posted: Sat Mar 06, 2010 3:36 pm
DX
Why?
There is such an easier way!
=O
Did you understand or still need more help?! o.0
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Posted: Sat Mar 06, 2010 4:28 pm
there are several ways to solve this problem 3nodding
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Posted: Sat Mar 06, 2010 4:34 pm
Well, true lol XD
Jus, see what I would have done was just subtract 7 from the 38cm and that would be 31 cm.
Then, I would divide it between Width and Length and I would get 15.5cm between the two but then since it has four sides I would divide each of those between two again because there is 2 width sides and 2 length and I would get 7.7cm on each side XD
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Posted: Sat Mar 06, 2010 4:35 pm
Oh, I forgot to add the 7 cm I took out before =O
That like never happens to me! X.X
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Posted: Sat Mar 06, 2010 5:06 pm
Not quite right sorry, It's very close though. This is a very creative way to do it 3nodding . I would have never thought of this.
Let me fix it. Your idea is to make our perimeter into a square, the problem is the equation for the perimeter is 2w+2l=38
(ie: w+w+(w+7)+(w+7)=38 ) so if we subtract 7 off of 38, we are only accounting for one of the long sides... We need to subtract off another 7 for the other long side. (ie: we can rearrange this to be w+w+w+w+14=38 ) So it should be
38-14=24.
(ie: w+w+w+w=24) where they are all equal. Then divide by 4 to see how long each of the equal sides like you suggested.
24/4=6
(ie: 6+6+6+6=24) so each side of the square sides has a length of 6. Add back in 7 to find out what one of the long sides has to be.
6+7=13
So each of the short sides are 6, and each of the long sides are 13. Which matches up with the answers I got before.
and as expected
6+6+13+13=38
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