Question

help please...

Marcie wants to enclose her yard with a fence. Her yard is in the shape of a triangle attached to a rectangle. See the figure below.
Yard is shapred like a square and a triangle.
The area of this figure can be found by the formula A = (wh) + 0.5(bh). If Marcie wants the total area to be larger than a specified value, she can use the formula A > (wh)+ 0.5(bh). Rewrite this formula to solve for b. Show all steps in your work.

Answer 1

please help... i will medal and fan!

Answer 2

@dan815 @AllTehMaffs @Unanimoose @k_lynn @bohotness

Answer 3

o.o

Answer 4

@phi

Answer 5

Do you have values, or are you just generally trying to solve for b?

Answer 6

i am just solving for b

Answer 7

Is the inequality (greater than sign) throwing you, or the rearranging in general? ^_^

Answer 8

yes it is mostly the inequality and since that confuses me, the whole equation has me thrown off

Answer 9

Cool cool. So, if you just had to solve the original equality
\[ A = (wh) + .5(bh)\]
what would it look like in terms of b?

Answer 10

is all you have to do is divide everything by (wh)+.5(h)

Answer 11

?

Answer 12

then just add the inequality back?

Answer 13

Not quite. Remember that if you divided by wh+.5h it would give you an angry looking fraction!

\[ \frac{A}{wh+.5(h)} = \frac{wh + .5(bh)}{wh+.5h}\]

yuck

You have to subtract the rectangle's area from both sides first, so the .5bh is alone on the left

Answer 14

Sorry, alone on the right

Answer 15

rectangle's area = wh

Answer 16

I'm having you do the normal equality first because operations on an inequality are almost exactly the same as an equality, with the only difference being that multiplying by a negative flips it - but we don't have to deal with that in this problem!

If you do all of the operations like you would in the normal equation and make sure that the inequality opens towards the A, you'll end up with the right answer.

Answer 17

oh ok i think i get it now... you have to subtract .5h from both sides the divide, right

Answer 18

So if we have
\[ A = wh + .5(bh)\]
you subtract the wh from both sides first to "get rid if it" on the right hand side, so you get
\[A - wh = \cancel{wh} - \cancel{wh} + .5(bh) \]
leaving you with
\[ A - wh = .5bh\]

Can you see the next step?

Answer 19

yup yup yup ^_^ So what does that give you?

Answer 20

b=-wh+a/.5h

Answer 21

Close close. Remember the parenthesis, so that it's
\[(A -wh) = .5bh\]
and everything on the left is divided by the .5h.

Then also, 1/.5 = 2
\[ \frac{1}{\frac{1}{2}} = 2\]

soooooo