Question

a flower bed is in the shape of a triangle with one side twice the length ofthe shortest side and the third side is 19 feel more than the length of the shortest side. Find the dimensions if the perimeter is 171 feet. a=_____ ft (shortest side)
b=_____ft (second side)
c=_______ft (third side)

Answer 1

One of the sides, the shortest side, is an unknown length, we'll call it \(\Large\bf\sf x\).
One of the other sides is twice that length, \(\Large\bf\sf 2x\).
The other side is \(\Large\bf\sf 19\).

The perimeter ( distance around the triangle ) is 171.
Do you remember how to find perimeter?

Answer 2

no this one i got wrong

Answer 3

Perimeter is the `distance around the triangle`.
So we'll just add up the lengths of the sides, that will give us perimeter.

\[\Large\bf\sf x+2x+19\quad=\quad P\]Understand how I set up the perimeter equation?
I added up all 3 sides to get perimeter.

Answer 4

They're telling us that the perimeter is 171.\[\Large\bf\sf x+2x+19\quad=\quad 171\]

Answer 5

what does thus mean?
i cant see any pictures

Answer 6

From here, we should be able to do some calculations and figure out what the value of \(\Large\bf\sf x\) our shortest side length is.

Answer 7

You can't see the math equations?
Are they just showing up as messy code?

Answer 8

\(\Large\bf\sf x\) and yes like this one

Answer 9

Grr.
Are you using Internet Explorer? :3

Answer 10

i using moozilla i think

Answer 11

Mmm ok I'll stop using the fancy math tool.
I guess it's not working properly again.

Answer 12

no its not woring at all

Answer 13

One of the sides, the shortest side, is an unknown length, we'll call it `x`.
One of the other sides is twice that length, `2x`.
The other side is `19`.

The perimeter ( distance around the triangle ) is `171`.

Using that information I'm setting up this equation:
`x` + `2x` + `19` = `171`

Do you understand how I set that up?
Perimeter is the sum of the 3 sides.

Answer 14

sohow do i find the answer to all 3

Answer 15

Recall that we decided to label the `shortest side` using `x`.

So if we can solve for `x`, we will have found one of our sides.
From there we might be able to figure the rest out.

Do you know how to solve for `x` in the equation that I set up?

Answer 16

no i need help on this part too

Answer 17

x and 2x are like terms, they can be combined.

x is the same as 1x.
Maybe thing of them as objects.
If you have 1 apple and add 2 apples, you get 3 apples right?

Answer 18

Therefore, x + 2x gives us 3x.

Answer 19

x + 2x + 19 = 171

Becomes,

3x + 19 = 171

From here, see how we're adding 19 on the side that includes x?
Let's do the inverse operation of addition to get rid of the 19.
So the inverse of addition is subtraction.
We'll subtract 19 from each side.

3x = 171 - 19

Understand those first two steps ok?

Answer 20

oksy got it

Answer 21

3x = 152

The 3 is multiplying the x.
The inverse of multiplication is division.
So let's divide each side by 3, that should get rid of the 3 on the left.

x = 152 / 3

Answer 22

50.67

Answer 23

And unfortunately this gives us an ugly ugly decimal >:[
Not sure why they're doing that to us...
If we write it as a mixed number, then x, our shortest side has a length of 50 and 2/3.

Answer 24

should i write the 2/3 part?

Answer 25

Hmm I made a boo boo somewhere, the shortest side would be the 19 side, not 50 and 2/3.
Mmm one sec... lemme see what's going on. Maybe I misread the question.

Answer 26

Oh derp...
Ya I misread it :(

The third side is `19 more than the shortest side`.

So our third side should be 19 + x.

So our perimeter formula should actually be:

`x` + `2x` + `19+x` = `171`

Answer 27

Grr sorry bout that :(

Answer 28

Again, solving for x, we'll combine like terms:

4x + 19 = 171

Then do some math, subtract 19,
4x = 152

Divide by 4,
x = 152/4

Answer 29

That will deal with our ugly decimal which is nice :o

Answer 30

38

Answer 31

Ok good! We've found the length of our shortest side.

Answer 32

One of the other sides has length `twice` as long as the shortest side.
Soooooo what would that be? :x

Answer 33

40

Answer 34

The shortest side is 38,
The other side is twice that long..

Hmm not sure where you're getting 40 from.

Answer 35

Twice means double the value.
Not + 2

Answer 36

so then 60

Answer 37

Hmm twice 38 should give us ummmm 76...

Answer 38

so 76
?

Answer 39

well what abut the next one the lst one