### Brain Teasers

# Some Algebra 2

The length of a rectangle is 9 centimeters more than half the width. Find the length if the perimeter is 60 centimeters.

### Hint

the length= 9+1/2 the width.60= 2width + 2 length

### Answer

Length is 16 cm and the width is 14 cm.Solution:

60cm=2width + 2 (9+1/2width)

Distribute the 2 and you get

60cm= 2width + 18 + 1width.

Combine the widths. And subtract 18 from both sides.

42cm= 3 width.

Divide both sides by 3 to get the length of the width.

Width=14cm. Then plug it into the equation for the length and you should get 16cm.

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## Comments

Working with numbers can be quite fun. Can't it? WTG, Crazy! Keep bringing on some more! This one is quite easy. But, it does get your mind started! WTG!

Hey thanks!

That was much more fun than it was in high school. Maybe I didn't appreciate it then? There's such a sense of accomplishment to solve algebra!-- and the highest maths I've taken are algebra 1 and geometry, so this makes me feel smart.

yey!

I must have done it wrong tho, but cant find it. I got L=24.

L=9c > 1/2w

4/60 = 15

15+9 = 24 for both sides

48-60 = w

w=6

what did i do wrong?

L=9c > 1/2w

4/60 = 15

15+9 = 24 for both sides

48-60 = w

w=6

what did i do wrong?

Using algebra:

Let the width be x cm.

Half the width is x/2 cm.

The length is x/2 + 9 cm.

Now the semi perimeter is 30 cm (length + width)

x + x/2 + 9 = 30

x + x/2 = 21

3x/2 = 21

3x = 42

x = 14 (width).

length = 14/2 + 9 = 7 + 9 = 16 cm.

Let the width be x cm.

Half the width is x/2 cm.

The length is x/2 + 9 cm.

Now the semi perimeter is 30 cm (length + width)

x + x/2 + 9 = 30

x + x/2 = 21

3x/2 = 21

3x = 42

x = 14 (width).

length = 14/2 + 9 = 7 + 9 = 16 cm.

Dec 05, 2006

WOW!!!!!!!!!!!!! I DIDN'T EVEN KNOW THAT

HEY! this was my 1000th "teaser"!!!

and... even being in Honors Alg 2 i managed to get it wrong! good job!

and... even being in Honors Alg 2 i managed to get it wrong! good job!

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